qu.1.topic=1-elementary indefinite integrals@ qu.1.1.mode=Formula Mod C@ qu.1.1.comment=The answer is \${mathml("\$answer")}.@ qu.1.1.editing=useHTML@ qu.1.1.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$a=range(1,9); \$n=range(1,4); \$m=range(2,5); \$k=range(4,9); condition:gt(\$k-\$m,1); \$pcoef=range(0,9); \$acoef=range(0,9); \$tcoef=range(0,9); \$tsgn=range(-1,1,2); condition:gt(\$pcoef*\$acoef+(\$pcoef+\$acoef)*\$tcoef,0); \$pnum=range(0,7); \$anum=range(0,1); \$tnum=range(0,2); \$pfnc=if(eq(\$pcoef,0),0,switch(\$pnum,\$pcoef*\$X^\$m*(\$X^\$n+\$X^(-\$k)),\$pcoef*\$X^\$m*(\$X^\$n+\$X^(-\$k)),\$pcoef*\$X^((2*\$n+1)/"2"),\$pcoef*\$X^((2*\$n+1)/"2"),\$pcoef/(\$X^\$m),\$pcoef/(\$X^\$m),\$pcoef/sqrt(\$X),\$pcoef*sqrt(\$X))); \$pans=switch(\$pnum,\$pcoef*(\$X^(\$m+\$n+1)/(\$m+\$n+1)-\$X^(\$m-\$k+1)/(\$k-\$m-1)),\$pcoef*(\$X^(\$m+\$n+1)/(\$m+\$n+1)-\$X^(\$m-\$k+1)/(\$k-\$m-1)),("2*\$pcoef"/(2*\$n+3))*\$X^((2*\$n+3)/"2"),("2*\$pcoef"/(2*\$n+3))*\$X^((2*\$n+3)/"2"),-("\$pcoef"/(\$m-1))*\$X^(1-\$m),-("\$pcoef"/(\$m-1))*\$X^(1-\$m),2*\$pcoef*sqrt(\$X),("2*\$pcoef"/3)*\$X^(3/"2")); \$afnc=if(eq(\$acoef,0),0,switch(\$anum,\$acoef/(1+\$X^2),\$acoef/sqrt(1-\$X^2))); \$aans=switch(\$anum,\$acoef*arctan(\$X),\$acoef*arcsin(\$X)); \$tfnc=\$tcoef*switch(\$tnum,sin(\$a*\$X),cos(\$a*\$X),"e"^(\$a*\$X)); \$tans=(\$tcoef/"\$a")*switch(\$tnum,cos(\$a*\$X),sin(\$a*\$X),"e"^(\$a*\$X)); \$function=if(eq(\$tsgn,1),switch(range(0,3),"\$pfnc+\$afnc+\$tfnc","\$afnc+\$pfnc+\$tfnc","\$tfnc+\$pfnc+\$afnc","\$tfnc+\$afnc+\$pfnc"),switch(range(0,3),"\$pfnc+\$afnc-\$tfnc","\$afnc+\$pfnc-\$tfnc","-\$tfnc+\$pfnc+\$afnc","-\$tfnc+\$afnc+\$pfnc")); \$anssgn=\$tsgn*if(eq(\$tnum,0),-1,1); \$answer=if(eq(\$anssgn,1),"\$pans+\$aans+\$tans","\$pans+\$aans-\$tans");@ qu.1.1.question=Compute $\int$ $\left[$ \${mathml("\$function")} $\right]$ \${mathml(d*\$X)}.@ qu.1.1.answer=\$answer@ qu.2.topic=2-elementary definite integrals@ qu.2.1.mode=Formula@ qu.2.1.comment=The answer is \${mathml("\$answer")}.@ qu.2.1.editing=useHTML@ qu.2.1.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$n=range(2,4); \$a=range(1,3); \$b=range(2,7-\$n); condition:lt(\$a,\$b); \$c=range(1,3); \$d=range(1,3); \$s=range(-1,1,2); \$G=if(eq(\$n,2),\$c*\$X+\$s*(\$d/\$X^2),\$c*\$X^(\$n-1)+\$s*(\$d/\$X^2)); \$F=(\$c*\$X^(\$n+1)+\$s*\$d)/\$X^2; \$function=switch(range(0,3),\$F,\$F,\$F,\$G); \$from=\$a; \$to=\$b; \$num=\$a*\$b*\$c*(\$b^\$n-\$a^\$n)+\$n*\$s*\$d*(\$b-\$a); \$den=\$n*\$a*\$b; \$answer=if(eq(gcd(\$num,\$den),\$den),\$num/\$den,\$num/"\$den");@ qu.2.1.question=Compute ${\int }_{from}^{to}$ $\left($ \${mathml(\$function)} $\right)$ \${mathml(d*\$X)}.@ qu.2.1.answer=\$answer@ qu.2.2.mode=Formula@ qu.2.2.comment=The answer is \${mathml("\$answer")}.@ qu.2.2.editing=useHTML@ qu.2.2.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$n=range(2,4); \$a=range(1,3); \$b=range(2,7-\$n); condition:lt(\$a,\$b); \$c=range(1,3); \$d=range(1,3); \$G=if(eq(\$n,2),\$c*\$X+\$d/sqrt(\$X),\$c*\$X^(\$n-1)+\$d/sqrt(\$X)); \$F=(\$c*\$X^\$n+\$d*sqrt(\$X))/\$X; \$function=switch(range(0,3),\$F,\$F,\$F,\$G); \$from=\$a; \$to=\$b; \$f=-if(eq(\$a,1),1,0)+if(eq(\$b,4),2,0); \$num=\$c*(\$b^\$n-\$a^\$n)+2*\$n*\$d*\$f; \$one=if(eq(gcd(\$num,\$n),\$n),\$num/\$n,"\$num/\$n"); \$answer=switch(\$f+1,"\$one"+2*\$d*"sqrt(\$b)","\$one"+2*\$d*"sqrt(\$b)"-2*\$d*"sqrt(\$a)","\$one","\$one"-2*\$d*"sqrt(\$a)");@ qu.2.2.question=Compute ${\int }_{from}^{to}$ $\left($ \${mathml(\$function)} $\right)$ \${mathml(d*\$X)}.@ qu.2.2.answer=\$answer@ qu.2.3.mode=Formula@ qu.2.3.comment=The answer is \${mathml("\$answer")}.@ qu.2.3.editing=useHTML@ qu.2.3.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$n=range(2,4); \$case=range(0,3); \$c=range(1,9); condition:not(eq(\$c,\$n)); \$d=range(1,9); \$s=range(-1,1,2); \$two=switch(range(0,1),(\$d/\$X),\$d*\$X^(-1)); \$G=if(eq(\$n,2),\$c*\$X+\$s*\$two,\$c*\$X^(\$n-1)+\$s*\$two); \$F=(\$c*\$X^\$n+\$s*\$d)/\$X; \$function=switch(range(0,3),\$F,\$F,\$F,\$G); \$from=switch(\$case,1,2,1,2); \$to=switch(\$case,"e","e",3,3); \$f=if(eq(gcd(\$c,\$n),\$n),\$c/\$n,"\$c/\$n"); \$num=switch(\$case,\$n*\$s*\$d-\$c,\$n*\$s*\$d-\$c*2^\$n,\$c*(3^\$n-1),\$c*(3^\$n-2^\$n)); \$k=if(eq(gcd(\$num,\$n),\$n),\$num/\$n,\$num/"\$n"); \$answer=switch(\$case,"\$k"+"\$f"*"e"^\$n,"\$k"+"\$f"*"e"^\$n-\$s*\$d*ln("2"),"\$k"+\$s*\$d*ln("3"),"\$k"+\$s*\$d*ln("3")-\$s*\$d*ln("2"));@ qu.2.3.question=Compute ${\int }_{from}^{to}$ $\left($ \${mathml(\$function)} $\right)$ \${mathml(d*\$X)}.@ qu.2.3.answer=\$answer@ qu.2.4.mode=Formula@ qu.2.4.comment=The answer is \${mathml("\$answer")}.@ qu.2.4.editing=useHTML@ qu.2.4.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$a=range(1,2); \$b=range(2,3); \$c=range(1,3); \$d=range(1,3); \$n=range(1,2); \$m=2*\$n; condition:lt(\$a,\$b); \$function=if(eq(\$n,1),\$c+\$d*sqrt(\$X),\$c*\$X+\$d*sqrt(\$X)); \$from=\$a^2; \$to=\$b^2; \$num=6*\$c*(\$b^\$m-\$a^\$m)/\$n+4*\$d*(\$b^3-\$a^3); \$answer=if(eq(gcd(\$num,6),6),\$num/6,"\$num/6");@ qu.2.4.question=Compute ${\int }_{from}^{to}$ $\left($ \${mathml(\$function)} $\right)$ \${mathml(d*\$X)}.@ qu.2.4.answer=\$answer@ qu.3.topic=3-indefinite substitution@ qu.3.1.mode=Formula Mod C@ qu.3.1.comment=The answer is \${mathml("\$answer")}.@ qu.3.1.editing=useHTML@ qu.3.1.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$a=range(1,6); \$b=range(1,6); condition:gt(\$a+\$b,2); \$n=range(2,5); \$r=range(0,5); \$w=switch(\$r,\$b*\$X^\$n,-\$b*\$X^\$n,(\$X+\$a)^\$n,\$b*sin(\$a*\$X),\$b*cos(\$a*\$X),\$b*sqrt(\$X)); \$wpf=switch(\$r,if(eq(\$n,2),\$X,\$X^(\$n-1)),if(eq(\$n,2),\$X,\$X^(\$n-1)),if(eq(\$n,2),\$X+\$a,(\$X+\$a)^(\$n-1)),cos(\$a*\$X),sin(\$a*\$X),sqrt(\$X)); \$wpcr=switch(\$r,"1"/(\$n*\$b),-("1"/(\$n*\$b)),"1"/\$n,"1"/(\$a*\$b),-("1"/(\$a*\$b)),"2"/\$b); \$function=if(lt(\$r,5),(\$wpf)*"e"^(\$w),("e"^(\$w))/\$wpf); \$answer="\$wpcr"*"e"^(\$w);@ qu.3.1.question=Compute $\int$ \${mathml("\$function")} \${mathml(d*\$X)}.@ qu.3.1.answer=\$answer@ qu.3.2.mode=Formula Mod C@ qu.3.2.comment=The answer is \${mathml("\$answer")}.@ qu.3.2.editing=useHTML@ qu.3.2.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$a=range(1,6); \$b=range(1,6); condition:gt(\$a+\$b,2); \$c=range(2,6); \$n=range(2,5); \$r=range(0,7); \$w=switch(\$r,\$c*\$X^\$n,\$a+\$b*\$X^\$n,\$b*\$X^\$n-\$a,\$a-\$b*\$X^\$n,\$c*"e"^\$X,\$a+\$b*"e"^\$X,\$c*ln(\$X),\$b*sqrt(\$X)); \$wpf=switch(\$r,if(eq(\$n,2),\$X,\$X^(\$n-1)),if(eq(\$n,2),\$X,\$X^(\$n-1)),if(eq(\$n,2),\$X,\$X^(\$n-1)),if(eq(\$n,2),\$X,\$X^(\$n-1)),"e"^\$X,"e"^\$X,\$X,sqrt(\$X)); \$wpcr=switch(\$r,"1"/(\$n*\$c),"1"/(\$n*\$b),"1"/(\$n*\$b),-("1"/(\$n*\$b)),"1"/\$c,"1"/\$b,"1"/\$c,"2"/\$b); \$function=if(lt(\$r,6),"\$wpf*cos(\$w)","cos(\$w)/\$wpf"); \$answer="\$wpcr*sin(\$w)";@ qu.3.2.question=Compute $\int$ \${mathml("\$function")} \${mathml(d*\$X)}.@ qu.3.2.answer=\$answer@ qu.3.3.mode=Formula Mod C@ qu.3.3.comment=The answer is \${mathml("\$answer")}.@ qu.3.3.editing=useHTML@ qu.3.3.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$a=range(1,6); \$b=range(1,6); condition:gt(\$a+\$b,2); \$c=range(2,6); \$n=range(2,5); \$r=range(0,7); \$w=switch(\$r,\$c*\$X^\$n,\$a+\$b*\$X^\$n,\$b*\$X^\$n-\$a,\$a-\$b*\$X^\$n,\$c*"e"^\$X,\$a+\$b*"e"^\$X,\$c*ln(\$X),\$b*sqrt(\$X)); \$wpf=switch(\$r,if(eq(\$n,2),\$X,\$X^(\$n-1)),if(eq(\$n,2),\$X,\$X^(\$n-1)),if(eq(\$n,2),\$X,\$X^(\$n-1)),if(eq(\$n,2),\$X,\$X^(\$n-1)),"e"^\$X,"e"^\$X,\$X,sqrt(\$X)); \$wpcnr=switch(\$r,-("1"/(\$n*\$c)),-("1"/(\$n*\$b)),-("1"/(\$n*\$b)),"1"/(\$n*\$b),-("1"/\$c),-("1"/\$b),-("1"/\$c),-("2"/\$b)); \$function=if(lt(\$r,6),"\$wpf*sin(\$w)","sin(\$w)/\$wpf"); \$answer="\$wpcnr*cos(\$w)";@ qu.3.3.question=Compute $\int$ \${mathml("\$function")} \${mathml(d*\$X)}.@ qu.3.3.answer=\$answer@ qu.3.4.mode=Formula Mod C@ qu.3.4.comment=The answer is \${mathml("\$answer")}.@ qu.3.4.editing=useHTML@ qu.3.4.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$a=range(1,6); \$b=range(1,6); condition:gt(\$a+\$b,2); \$c=range(2,6); \$k=range(-1,1,2)*range(1,2); \$n=range(2,5); \$m=range(2,5); \$r=range(0,14); \$w=switch(\$r,\$a+\$b*\$X^\$n,\$b*\$X^\$n-\$a,\$a-\$b*\$X^\$n,\$a+\$b*"e"^(\$k*\$X),\$b*"e"^(\$k*\$X)-\$a,\$a-\$b*"e"^\$X,sin(\$c*\$X),cos(\$c*\$X),\$a+sin(\$X),\$a-sin(\$X),\$a-cos(\$X),\$a+cos(\$X),ln(\$X),\$a+ln(\$X),\$a-ln(\$X)); \$wpf=switch(\$r,if(eq(\$n,2),\$X,\$X^(\$n-1)),if(eq(\$n,2),\$X,\$X^(\$n-1)),if(eq(\$n,2),\$X,\$X^(\$n-1)),"e"^(\$k*\$X),"e"^(\$k*\$X),"e"^\$X,cos(\$c*\$X),sin(\$c*\$X),cos(\$X),cos(\$X),sin(\$X),sin(\$X),\$X,\$X,\$X); \$wpc=switch(\$r,\$n*\$b,\$n*\$b,-\$n*\$b,\$b*\$k,\$b*\$k,-\$b,\$c,-\$c,1,-1,1,-1,1,1,-1); \$function=if(lt(\$r,12),("\$wpf")*("\$w")^\$m,(("\$w")^\$m)/\$wpf); \$answer=("1"/((\$wpc)*(\$m+1)))*("\$w"^(\$m+1));@ qu.3.4.question=Compute $\int$ \${mathml("\$function")} \${mathml(d*\$X)}.@ qu.3.4.answer=\$answer@ qu.3.5.mode=Formula Mod C@ qu.3.5.comment=The answer is \${mathml("\$answer")}.@ qu.3.5.editing=useHTML@ qu.3.5.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$a=range(1,6); \$b=range(1,6); condition:gt(\$a+\$b,2); \$c=range(2,6); \$k=range(-1,1,2)*range(1,2); \$n=range(2,5); \$m=range(2,5); \$r=range(0,14); \$w=switch(\$r,\$a+\$b*\$X^\$n,\$b*\$X^\$n-\$a,\$a-\$b*\$X^\$n,\$a+\$b*"e"^(\$k*\$X),\$b*"e"^(\$k*\$X)-\$a,\$a-\$b*"e"^\$X,sin(\$c*\$X),cos(\$c*\$X),\$a+sin(\$X),\$a-sin(\$X),\$a-cos(\$X),\$a+cos(\$X),ln(\$X),\$a+ln(\$X),\$a-ln(\$X)); \$wpf=switch(\$r,if(eq(\$n,2),\$X,\$X^(\$n-1)),if(eq(\$n,2),\$X,\$X^(\$n-1)),if(eq(\$n,2),\$X,\$X^(\$n-1)),"e"^(\$k*\$X),"e"^(\$k*\$X),"e"^\$X,cos(\$c*\$X),sin(\$c*\$X),cos(\$X),cos(\$X),sin(\$X),sin(\$X),\$X,\$X,\$X); \$wpc=switch(\$r,\$n*\$b,\$n*\$b,-\$n*\$b,\$b*\$k,\$b*\$k,-\$b,\$c,-\$c,1,-1,1,-1,1,1,-1); \$function=if(lt(\$r,12),("\$wpf")/sqrt("\$w"),1/(\$wpf*sqrt("\$w"))); \$answer=("2"/(\$wpc))*sqrt("\$w");@ qu.3.5.question=Compute $\int$ \${mathml("\$function")} \${mathml(d*\$X)}.@ qu.3.5.answer=\$answer@ qu.3.6.mode=Formula Mod C@ qu.3.6.comment=The answer is \${mathml("\$answer")}.@ qu.3.6.editing=useHTML@ qu.3.6.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$a=range(1,6); \$b=range(1,6); condition:gt(\$a+\$b,2); \$c=range(2,6); \$k=range(-1,1,2)*range(1,2); \$n=range(2,5); \$m=range(2,5); \$r=range(0,14); \$w=switch(\$r,\$a+\$b*\$X^\$n,\$b*\$X^\$n-\$a,\$a-\$b*\$X^\$n,\$a+\$b*"e"^(\$k*\$X),\$b*"e"^(\$k*\$X)-\$a,\$a-\$b*"e"^\$X,sin(\$c*\$X),cos(\$c*\$X),\$a+sin(\$X),\$a-sin(\$X),\$a-cos(\$X),\$a+cos(\$X),ln(\$X),\$a+ln(\$X),\$a-ln(\$X)); \$wpf=switch(\$r,if(eq(\$n,2),\$X,\$X^(\$n-1)),if(eq(\$n,2),\$X,\$X^(\$n-1)),if(eq(\$n,2),\$X,\$X^(\$n-1)),"e"^(\$k*\$X),"e"^(\$k*\$X),"e"^\$X,cos(\$c*\$X),sin(\$c*\$X),cos(\$X),cos(\$X),sin(\$X),sin(\$X),\$X,\$X,\$X); \$wpc=switch(\$r,\$n*\$b,\$n*\$b,-\$n*\$b,\$b*\$k,\$b*\$k,-\$b,\$c,-\$c,1,-1,1,-1,1,1,-1); \$function=if(lt(\$r,12),("\$wpf")/("\$w")^2,1/(\$wpf*("\$w")^2)); \$answer=if(gt(\$wpc,0),"-1"/(\$wpc*("\$w")),"1"/(-\$wpc*("\$w")) );@ qu.3.6.question=Compute $\int$ \${mathml("\$function")} \${mathml(d*\$X)}.@ qu.3.6.answer=\$answer@ qu.4.topic=4-definite substitution@ qu.4.1.mode=Formula@ qu.4.1.comment=The answer is \${mathml("\$answer")}.@ qu.4.1.editing=useHTML@ qu.4.1.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$a=range(1,2); \$b=range(1,3); condition:gt(\$a+\$b,2); \$n=range(4,6); \$m=\$n-1; \$r=range(0,2); \$w=switch(\$r,\$a+\$b*\$X,\$b*\$X+\$a,\$b*\$X-\$a); \$function=(\$w)^\$m; \$from=range(0,1); \$to=range(1,3)+\$from; condition:gt(\$to,1); \$num=if(eq(\$r,2),"(\$b*\$to-\$a)^\$n"-(\$b*\$from-\$a)^\$n,if(eq(\$from,0),"(\$b*\$to+\$a)^\$n"-(\$b*\$from+\$a)^\$n,"(\$b*\$to+\$a)^\$n-(\$b*\$from+\$a)^\$n")); \$answer="\$num"/(\$b*\$n);@ qu.4.1.question=Compute ${\int }_{from}^{to}$ \${mathml(\$function)} \${mathml(d*\$X)}.@ qu.4.1.answer=\$answer@ qu.4.2.mode=Formula@ qu.4.2.comment=The answer is \${mathml("\$answer")}.@ qu.4.2.editing=useHTML@ qu.4.2.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$a=range(2,5); \$b=range(1,5); \$n=range(2,5); \$r=range(0,2); \$t=range(2,4); condition:not(gt(\$t+\$n,6)); \$s=switch(\$r,1,1,-1); \$q=switch(\$r,7,1,\$t^\$n); condition:gt(\$s*\$b*\$q,\$s*\$a); \$w=switch(\$r,\$a+\$b*\$X^\$n,\$b*\$X^\$n-\$a,\$a-\$b*\$X^\$n); \$wpf=switch(\$r,if(eq(\$n,2),\$X,\$X^(\$n-1)),if(eq(\$n,2),\$X,\$X^(\$n-1)),if(eq(\$n,2),\$X,\$X^(\$n-1))); \$wpc=switch(\$r,\$n*\$b,\$n*\$b,-\$n*\$b); \$function=(\$wpf)/(\$w); \$from=switch(\$r,0,1,0); \$to=\$t; \$wto=switch(\$r,\$a+\$b*\$to^\$n,\$b*\$to^\$n-\$a,\$a-\$b*\$to^\$n); \$wfrom=switch(\$r,\$a,\$b-\$a,\$a); \$answer=("1"/(\$wpc))*"ln(\$wto/\$wfrom)";@ qu.4.2.question=Compute ${\int }_{from}^{to}$ \${mathml(\$function)} \${mathml(d*\$X)}.@ qu.4.2.answer=\$answer@ qu.4.3.mode=Formula@ qu.4.3.comment=The answer is \${mathml("\$answer")}.@ qu.4.3.editing=useHTML@ qu.4.3.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$a=range(2,5); \$b=range(1,6); \$r=range(0,2); \$t=range(1,3); \$s=switch(\$r,1,1,-1); \$p=switch(\$r,2,0,\$t); condition:gt(\$s*\$b*e^\$p,\$s*\$a); \$w=switch(\$r,\$a+\$b*"e"^\$X,\$b*"e"^\$X-\$a,\$a-\$b*"e"^\$X); \$wpf="e"^\$X; \$wpc=switch(\$r,\$b,\$b,-\$b); \$function=("\$wpf")/("\$w"); \$from=0; \$to=\$t; \$wto=switch(\$r,\$a+\$b*"e"^\$to,\$b*"e"^\$to-\$a,\$a-\$b*"e"^\$to); \$wfrom=switch(\$r,\$a+\$b,\$b-\$a,\$a-\$b); \$answer=if(eq(\$wfrom,1),("1"/(\$wpc))*"ln(\$wto)",("1"/(\$wpc))*"ln((\$wto)/(\$wfrom))");@ qu.4.3.question=Compute ${\int }_{from}^{to}$ \${mathml("\$function")} \${mathml(d*\$X)}.@ qu.4.3.answer=\$answer@ qu.4.4.mode=Formula@ qu.4.4.comment=The answer is \${mathml("\$answer")}.@ qu.4.4.editing=useHTML@ qu.4.4.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$a=range(2,5); \$c=range(2,5); \$r=range(0,4); \$rd=range(0,3); condition:gt(\$r+\$rd,0); \$w=switch(\$r,cos(\$c*\$X),\$a+sin(\$X),\$a-sin(\$X),\$a-cos(\$X),\$a+cos(\$X)); \$wpf=switch(\$r,sin(\$c*\$X),cos(\$X),cos(\$X),sin(\$X),sin(\$X)); \$wpc=switch(\$r,-\$c,1,-1,1,-1); \$function=if(eq(\$r,0),tan(\$c*\$X),(\$wpf)/(\$w)); \$from=0; \$d=switch(\$rd,2,3,4,6); \$dento=if(eq(\$r,0),\$c*\$d,\$d); \$sin=switch(\$rd,2,"sqrt(3)","sqrt(2)",1); \$cos=switch(\$rd,0,1,"sqrt(2)","sqrt(3)"); \$wto=switch(\$r,"\$cos",2*\$a+"\$sin",2*\$a-"\$sin",2*\$a-"\$cos",2*\$a+"\$cos"); \$wfrom=switch(\$r,2,2*\$a,2*\$a,2*\$a-2,2*\$a+2); \$answer=if(eq(\$wfrom,1),("1"/(\$wpc))*"ln(\$wto)",("1"/(\$wpc))*"ln((\$wto)/(\$wfrom))");@ qu.4.4.question=Compute ${\int }_{from}^{\pi /dento}$ \${mathml(\$function)} \${mathml(d*\$X)}.@ qu.4.4.answer=\$answer@ qu.4.5.mode=Formula@ qu.4.5.comment=The answer is \${mathml("\$answer")}.@ qu.4.5.editing=useHTML@ qu.4.5.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$a=range(2,5); \$n=range(2,5); \$m=\$n-1; \$r=range(0,1); \$function=switch(\$r,if(eq(\$m,1),\$X/(1+\$X^4),\$X^\$m/(1+\$X^(2*\$n))),1/(1+\$a^2*\$X^2)); \$from=range(0,1); \$to=range(1,3)+\$from; condition:gt(\$to,1); \$answer=switch(\$r,switch(\$from,"(arctan(\$to^\$n))"/\$n,"(4*arctan(\$to^\$n)-pi)"/(4*\$n)),switch(\$from,"(arctan(\$a*\$to))"/\$a,"(arctan(\$a*\$to)-arctan(\$a))"/\$a));@ qu.4.5.question=Compute ${\int }_{from}^{to}$ \${mathml(\$function)} \${mathml(d*\$X)}.@ qu.4.5.answer=\$answer@ qu.5.topic=5-integration by parts@ qu.5.1.mode=Formula Mod C@ qu.5.1.comment=The answer is \${mathml("\$answer")}.@ qu.5.1.editing=useHTML@ qu.5.1.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$a=range(1,9); \$b=range(1,9); \$c=range(-9,9); \$d=range(-9,9); condition:eq((\$a-1)*\$c*\$d,0); condition:not(eq((\$a-1)*(\$c+\$d)+\$c*\$d,0)); \$function=(\$b*\$X+\$d)*cos(\$a*\$X+\$c); \$A=\$a/gcd(\$a,\$b); \$B=\$b/gcd(\$a,\$b); \$term=if(eq(\$A,1),\$B*\$X,(\$B*\$X)/(\$A)); \$answer=(\$term+("\$d")/(\$a))*sin(\$a*\$X+\$c)+(("\$b")/(\$a^2))*cos(\$a*\$X+\$c);@ qu.5.1.question=Compute $\int$ \${mathml(\$function)} \${mathml(d*\$X)}.@ qu.5.1.answer=\$answer@ qu.5.2.mode=Formula Mod C@ qu.5.2.comment=The answer is \${mathml("\$answer")}.@ qu.5.2.editing=useHTML@ qu.5.2.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$a=range(1,9); \$b=range(1,9); \$c=range(-9,9); \$d=range(-9,9); condition:eq((\$a-1)*\$c*\$d,0); condition:not(eq((\$a-1)*(\$c+\$d)+\$c*\$d,0)); \$function=(\$b*\$X+\$d)*sin(\$a*\$X+\$c); \$A=\$a/gcd(\$a,\$b); \$B=\$b/gcd(\$a,\$b); \$term=if(eq(\$A,1),\$B*\$X,(\$B*\$X)/(\$A)); \$answer=-(\$term+("\$d")/(\$a))*cos(\$a*\$X+\$c)+(("\$b")/(\$a^2))*sin(\$a*\$X+\$c);@ qu.5.2.question=Compute $\int$ \${mathml(\$function)} \${mathml(d*\$X)}.@ qu.5.2.answer=\$answer@ qu.5.3.mode=Formula Mod C@ qu.5.3.comment=The answer is \${mathml("\$answer")}.@ qu.5.3.editing=useHTML@ qu.5.3.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$b=range(1,9); \$d=range(-9,9); \$k=range(-9,9); \$q=\$k*\$d-\$b; condition:not(eq(\$q*\$k*(\$k-1),0)); condition:gt(max(\$k,\$q),0); \$function=(\$b*\$X+\$d)*"e"^(\$k*\$X); \$a=abs(\$k); \$s=\$k/\$a; \$D=gcd(\$a,\$b); \$A=\$a/\$D; \$B=\$b/\$D; \$xt=if(eq(\$A,1),\$B*\$X,(\$B*\$X)/(\$A)); \$answer=if(eq(\$s,1),(\$xt+"\$q"/\$k^2)*"e"^(\$k*\$X),("\$q"/\$k^2-\$xt)*"e"^(\$k*\$X));@ qu.5.3.question=Compute $\int$ \${mathml("\$function")} \${mathml(d*\$X)}.@ qu.5.3.answer=\$answer@ qu.5.4.mode=Formula Mod C@ qu.5.4.comment=The answer is \${mathml("\$answer")}.@ qu.5.4.editing=useHTML@ qu.5.4.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$b=range(1,9); \$p=range(-9,9); condition:not(eq(\$p,0)); \$r=range(0,11); \$n=switch(\$r,2,4,6,8,10,12,-4,-6,3,5,1,-1); \$q=\$n/2; \$case=switch(\$r,0,1,1,1,1,1,2,2,3,3,4,5); \$function=switch(\$case,(\$b*\$X+\$p)*ln(\$X),(\$b*\$X^\$q+\$p)*ln(\$X),\$b*(ln(\$X)/\$X^(-\$q)),\$b*\$X^("\$n/2")*ln(\$X),\$b*sqrt(\$X)*ln(\$X),\$b*(ln(\$X)/sqrt(\$X))); \$c=if(lt(\$case,2),\$p,0); \$answer=((("2*\$b")/(\$n+2))*\$X^((\$n+2)/"2")+\$c*\$X)*ln(\$X)-((("4*\$b")/(\$n+2)^2)*\$X^((\$n+2)/"2")+\$c*\$X);@ qu.5.4.question=Compute $\int$ \${mathml("\$function")} \${mathml(d*\$X)}.@ qu.5.4.answer=\$answer@ qu.5.5.mode=Formula Mod C@ qu.5.5.comment=The answer is \${mathml("\$answer")}.@ qu.5.5.editing=useHTML@ qu.5.5.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$a=range(1,9); \$b=range(-9,9); condition:not(eq(\$b*(\$b^2+\$a-2),0)); \$r=range(0,1); \$fnc=switch(\$r,arctan(\$a*\$X),arcsin(\$a*\$X)); \$function=\$b*\$fnc; \$anszero=if(gt(\$b,0),\$b*\$X*\$fnc-("\$b/(2*\$a)")*ln(1+\$a^2*\$X^2),\$b*\$X*\$fnc+("-\$b/(2*\$a)")*ln(1+\$a^2*\$X^2)); \$ansone=if(gt(\$b,0),\$b*\$X*\$fnc+("\$b/\$a")*sqrt(1-\$a^2*\$X^2),\$b*\$X*\$fnc-("-\$b/\$a")*sqrt(1-\$a^2*\$X^2)); \$answer=switch(\$r,"\$anszero","\$ansone");@ qu.5.5.question=Compute $\int$ \${mathml("\$function")} \${mathml(d*\$X)}.@ qu.5.5.answer=\$answer@ qu.6.topic=6-quadratic denominators@ qu.6.1.mode=Formula Mod C@ qu.6.1.comment=The answer is \${mathml("\$answer")}.@ qu.6.1.editing=useHTML@ qu.6.1.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$a=range(-6,1); \$b=\$a+range(1,5); \$c=range(-4,4); \$d=range(-9,9); \$k=2*\$a*\$c+\$d; \$p=2*\$b*\$c+\$d; condition:not(eq(\$c*\$k*\$p*(\$a*\$c+\$b*\$c+\$d),0)); \$function=(2*\$c*\$X+\$d)/(\$X^2-(\$a+\$b)*\$X+\$a*\$b); \$ansone=((\$p)/"(\$b-\$a)")*ln(abs(\$X-\$b))-((\$k)/"(\$b-\$a)")*ln(abs(\$X-\$a)); \$anstwo=((\$p)/"(\$b-\$a)")*ln(abs(\$X-\$b))+((-\$k)/"(\$b-\$a)")*ln(abs(\$X-\$a)); \$answer=if(gt(\$k,0),"\$ansone","\$anstwo");@ qu.6.1.question=Compute $\int$ \${mathml(\$function)} \${mathml(d*\$X)}.@ qu.6.1.answer=\$answer@ qu.6.2.mode=Formula Mod C@ qu.6.2.comment=The answer is \${mathml("\$answer")}.@ qu.6.2.editing=useHTML@ qu.6.2.algorithm=\$V=switch(rint(7),"t","u","v","w","x","y","z"); \$X=\$V; \$a=range(1,5); \$b=range(-4,4); \$c=range(1,9); \$d=range(-9,9); condition:not(eq(\$b*(2*\$b*\$c+\$d),0)); \$function=(2*\$c*\$X+\$d)/(\$X^2-(2*\$b)*\$X+(\$a^2+\$b^2)); \$arg=if(eq(\$a,1),\$X-\$b,(\$X-\$b)/\$a); \$k=2*\$b*\$c+\$d; \$ansone=\$c*ln((\$X-\$b)^2+\$a^2)+((\$k)/"\$a")*arctan(\$arg); \$anstwo=\$c*ln((\$X-\$b)^2+\$a^2)-((-\$k)/"\$a")*arctan(\$arg); \$answer=if(gt(\$k,0),"\$ansone","\$anstwo");@ qu.6.2.question=Compute $\int$ \${mathml(\$function)} \${mathml(d*\$X)}.@ qu.6.2.answer=\$answer@