1,1,57,0,0.0171281,"\int x^2 \sin \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*Sin[a + b*Log[c*x^n]],x]","\frac{3 x^3 \sin \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+9}-\frac{b n x^3 \cos \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+9}","\frac{3 x^3 \sin \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+9}-\frac{b n x^3 \cos \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+9}",1,"-((b*n*x^3*Cos[a + b*Log[c*x^n]])/(9 + b^2*n^2)) + (3*x^3*Sin[a + b*Log[c*x^n]])/(9 + b^2*n^2)","A",1,1,15,0.06667,1,"{4485}"
2,1,57,0,0.0126992,"\int x \sin \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Sin[a + b*Log[c*x^n]],x]","\frac{2 x^2 \sin \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+4}-\frac{b n x^2 \cos \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+4}","\frac{2 x^2 \sin \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+4}-\frac{b n x^2 \cos \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+4}",1,"-((b*n*x^2*Cos[a + b*Log[c*x^n]])/(4 + b^2*n^2)) + (2*x^2*Sin[a + b*Log[c*x^n]])/(4 + b^2*n^2)","A",1,1,13,0.07692,1,"{4485}"
3,1,52,0,0.0112486,"\int \sin \left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sin[a + b*Log[c*x^n]],x]","\frac{x \sin \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+1}-\frac{b n x \cos \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+1}","\frac{x \sin \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+1}-\frac{b n x \cos \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+1}",1,"-((b*n*x*Cos[a + b*Log[c*x^n]])/(1 + b^2*n^2)) + (x*Sin[a + b*Log[c*x^n]])/(1 + b^2*n^2)","A",1,1,11,0.09091,1,"{4475}"
4,1,19,0,0.0151146,"\int \frac{\sin \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Sin[a + b*Log[c*x^n]]/x,x]","-\frac{\cos \left(a+b \log \left(c x^n\right)\right)}{b n}","-\frac{\cos \left(a+b \log \left(c x^n\right)\right)}{b n}",1,"-(Cos[a + b*Log[c*x^n]]/(b*n))","A",2,1,15,0.06667,1,"{2638}"
5,1,57,0,0.0178563,"\int \frac{\sin \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[Sin[a + b*Log[c*x^n]]/x^2,x]","-\frac{\sin \left(a+b \log \left(c x^n\right)\right)}{x \left(b^2 n^2+1\right)}-\frac{b n \cos \left(a+b \log \left(c x^n\right)\right)}{x \left(b^2 n^2+1\right)}","-\frac{\sin \left(a+b \log \left(c x^n\right)\right)}{x \left(b^2 n^2+1\right)}-\frac{b n \cos \left(a+b \log \left(c x^n\right)\right)}{x \left(b^2 n^2+1\right)}",1,"-((b*n*Cos[a + b*Log[c*x^n]])/((1 + b^2*n^2)*x)) - Sin[a + b*Log[c*x^n]]/((1 + b^2*n^2)*x)","A",1,1,15,0.06667,1,"{4485}"
6,1,57,0,0.0153199,"\int \frac{\sin \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[Sin[a + b*Log[c*x^n]]/x^3,x]","-\frac{2 \sin \left(a+b \log \left(c x^n\right)\right)}{x^2 \left(b^2 n^2+4\right)}-\frac{b n \cos \left(a+b \log \left(c x^n\right)\right)}{x^2 \left(b^2 n^2+4\right)}","-\frac{2 \sin \left(a+b \log \left(c x^n\right)\right)}{x^2 \left(b^2 n^2+4\right)}-\frac{b n \cos \left(a+b \log \left(c x^n\right)\right)}{x^2 \left(b^2 n^2+4\right)}",1,"-((b*n*Cos[a + b*Log[c*x^n]])/((4 + b^2*n^2)*x^2)) - (2*Sin[a + b*Log[c*x^n]])/((4 + b^2*n^2)*x^2)","A",1,1,15,0.06667,1,"{4485}"
7,1,97,0,0.031048,"\int x^2 \sin ^2\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*Sin[a + b*Log[c*x^n]]^2,x]","\frac{3 x^3 \sin ^2\left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+9}-\frac{2 b n x^3 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+9}+\frac{2 b^2 n^2 x^3}{3 \left(4 b^2 n^2+9\right)}","\frac{3 x^3 \sin ^2\left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+9}-\frac{2 b n x^3 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+9}+\frac{2 b^2 n^2 x^3}{3 \left(4 b^2 n^2+9\right)}",1,"(2*b^2*n^2*x^3)/(3*(9 + 4*b^2*n^2)) - (2*b*n*x^3*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/(9 + 4*b^2*n^2) + (3*x^3*Sin[a + b*Log[c*x^n]]^2)/(9 + 4*b^2*n^2)","A",2,2,17,0.1176,1,"{4487, 30}"
8,1,98,0,0.0222139,"\int x \sin ^2\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Sin[a + b*Log[c*x^n]]^2,x]","\frac{x^2 \sin ^2\left(a+b \log \left(c x^n\right)\right)}{2 \left(b^2 n^2+1\right)}-\frac{b n x^2 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{2 \left(b^2 n^2+1\right)}+\frac{b^2 n^2 x^2}{4 \left(b^2 n^2+1\right)}","\frac{x^2 \sin ^2\left(a+b \log \left(c x^n\right)\right)}{2 \left(b^2 n^2+1\right)}-\frac{b n x^2 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{2 \left(b^2 n^2+1\right)}+\frac{b^2 n^2 x^2}{4 \left(b^2 n^2+1\right)}",1,"(b^2*n^2*x^2)/(4*(1 + b^2*n^2)) - (b*n*x^2*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/(2*(1 + b^2*n^2)) + (x^2*Sin[a + b*Log[c*x^n]]^2)/(2*(1 + b^2*n^2))","A",2,2,15,0.1333,1,"{4487, 30}"
9,1,88,0,0.0187392,"\int \sin ^2\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sin[a + b*Log[c*x^n]]^2,x]","\frac{x \sin ^2\left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+1}-\frac{2 b n x \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+1}+\frac{2 b^2 n^2 x}{4 b^2 n^2+1}","\frac{x \sin ^2\left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+1}-\frac{2 b n x \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+1}+\frac{2 b^2 n^2 x}{4 b^2 n^2+1}",1,"(2*b^2*n^2*x)/(1 + 4*b^2*n^2) - (2*b*n*x*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/(1 + 4*b^2*n^2) + (x*Sin[a + b*Log[c*x^n]]^2)/(1 + 4*b^2*n^2)","A",2,2,13,0.1538,1,"{4477, 8}"
10,1,39,0,0.0304173,"\int \frac{\sin ^2\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Sin[a + b*Log[c*x^n]]^2/x,x]","\frac{\log (x)}{2}-\frac{\sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{2 b n}","\frac{\log (x)}{2}-\frac{\sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{2 b n}",1,"Log[x]/2 - (Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/(2*b*n)","A",3,2,17,0.1176,1,"{2635, 8}"
11,1,95,0,0.0258384,"\int \frac{\sin ^2\left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[Sin[a + b*Log[c*x^n]]^2/x^2,x]","-\frac{\sin ^2\left(a+b \log \left(c x^n\right)\right)}{x \left(4 b^2 n^2+1\right)}-\frac{2 b n \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{x \left(4 b^2 n^2+1\right)}-\frac{2 b^2 n^2}{x \left(4 b^2 n^2+1\right)}","-\frac{\sin ^2\left(a+b \log \left(c x^n\right)\right)}{x \left(4 b^2 n^2+1\right)}-\frac{2 b n \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{x \left(4 b^2 n^2+1\right)}-\frac{2 b^2 n^2}{x \left(4 b^2 n^2+1\right)}",1,"(-2*b^2*n^2)/((1 + 4*b^2*n^2)*x) - (2*b*n*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/((1 + 4*b^2*n^2)*x) - Sin[a + b*Log[c*x^n]]^2/((1 + 4*b^2*n^2)*x)","A",2,2,17,0.1176,1,"{4487, 30}"
12,1,98,0,0.0260508,"\int \frac{\sin ^2\left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[Sin[a + b*Log[c*x^n]]^2/x^3,x]","-\frac{\sin ^2\left(a+b \log \left(c x^n\right)\right)}{2 x^2 \left(b^2 n^2+1\right)}-\frac{b n \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{2 x^2 \left(b^2 n^2+1\right)}-\frac{b^2 n^2}{4 x^2 \left(b^2 n^2+1\right)}","-\frac{\sin ^2\left(a+b \log \left(c x^n\right)\right)}{2 x^2 \left(b^2 n^2+1\right)}-\frac{b n \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{2 x^2 \left(b^2 n^2+1\right)}-\frac{b^2 n^2}{4 x^2 \left(b^2 n^2+1\right)}",1,"-(b^2*n^2)/(4*(1 + b^2*n^2)*x^2) - (b*n*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/(2*(1 + b^2*n^2)*x^2) - Sin[a + b*Log[c*x^n]]^2/(2*(1 + b^2*n^2)*x^2)","A",2,2,17,0.1176,1,"{4487, 30}"
13,1,160,0,0.0553367,"\int x^2 \sin ^3\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*Sin[a + b*Log[c*x^n]]^3,x]","\frac{x^3 \sin ^3\left(a+b \log \left(c x^n\right)\right)}{3 \left(b^2 n^2+1\right)}+\frac{2 b^2 n^2 x^3 \sin \left(a+b \log \left(c x^n\right)\right)}{b^4 n^4+10 b^2 n^2+9}-\frac{2 b^3 n^3 x^3 \cos \left(a+b \log \left(c x^n\right)\right)}{3 \left(b^4 n^4+10 b^2 n^2+9\right)}-\frac{b n x^3 \sin ^2\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{3 \left(b^2 n^2+1\right)}","\frac{x^3 \sin ^3\left(a+b \log \left(c x^n\right)\right)}{3 \left(b^2 n^2+1\right)}+\frac{2 b^2 n^2 x^3 \sin \left(a+b \log \left(c x^n\right)\right)}{b^4 n^4+10 b^2 n^2+9}-\frac{2 b^3 n^3 x^3 \cos \left(a+b \log \left(c x^n\right)\right)}{3 \left(b^4 n^4+10 b^2 n^2+9\right)}-\frac{b n x^3 \sin ^2\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{3 \left(b^2 n^2+1\right)}",1,"(-2*b^3*n^3*x^3*Cos[a + b*Log[c*x^n]])/(3*(9 + 10*b^2*n^2 + b^4*n^4)) + (2*b^2*n^2*x^3*Sin[a + b*Log[c*x^n]])/(9 + 10*b^2*n^2 + b^4*n^4) - (b*n*x^3*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]]^2)/(3*(1 + b^2*n^2)) + (x^3*Sin[a + b*Log[c*x^n]]^3)/(3*(1 + b^2*n^2))","A",2,2,17,0.1176,1,"{4487, 4485}"
14,1,158,0,0.0448578,"\int x \sin ^3\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Sin[a + b*Log[c*x^n]]^3,x]","\frac{2 x^2 \sin ^3\left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+4}+\frac{12 b^2 n^2 x^2 \sin \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4+40 b^2 n^2+16}-\frac{6 b^3 n^3 x^2 \cos \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4+40 b^2 n^2+16}-\frac{3 b n x^2 \sin ^2\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+4}","\frac{2 x^2 \sin ^3\left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+4}+\frac{12 b^2 n^2 x^2 \sin \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4+40 b^2 n^2+16}-\frac{6 b^3 n^3 x^2 \cos \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4+40 b^2 n^2+16}-\frac{3 b n x^2 \sin ^2\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+4}",1,"(-6*b^3*n^3*x^2*Cos[a + b*Log[c*x^n]])/(16 + 40*b^2*n^2 + 9*b^4*n^4) + (12*b^2*n^2*x^2*Sin[a + b*Log[c*x^n]])/(16 + 40*b^2*n^2 + 9*b^4*n^4) - (3*b*n*x^2*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]]^2)/(4 + 9*b^2*n^2) + (2*x^2*Sin[a + b*Log[c*x^n]]^3)/(4 + 9*b^2*n^2)","A",2,2,15,0.1333,1,"{4487, 4485}"
15,1,149,0,0.0365887,"\int \sin ^3\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sin[a + b*Log[c*x^n]]^3,x]","\frac{x \sin ^3\left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+1}+\frac{6 b^2 n^2 x \sin \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4+10 b^2 n^2+1}-\frac{6 b^3 n^3 x \cos \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4+10 b^2 n^2+1}-\frac{3 b n x \sin ^2\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+1}","\frac{x \sin ^3\left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+1}+\frac{6 b^2 n^2 x \sin \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4+10 b^2 n^2+1}-\frac{6 b^3 n^3 x \cos \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4+10 b^2 n^2+1}-\frac{3 b n x \sin ^2\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+1}",1,"(-6*b^3*n^3*x*Cos[a + b*Log[c*x^n]])/(1 + 10*b^2*n^2 + 9*b^4*n^4) + (6*b^2*n^2*x*Sin[a + b*Log[c*x^n]])/(1 + 10*b^2*n^2 + 9*b^4*n^4) - (3*b*n*x*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]]^2)/(1 + 9*b^2*n^2) + (x*Sin[a + b*Log[c*x^n]]^3)/(1 + 9*b^2*n^2)","A",2,2,13,0.1538,1,"{4477, 4475}"
16,1,43,0,0.0317094,"\int \frac{\sin ^3\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Sin[a + b*Log[c*x^n]]^3/x,x]","\frac{\cos ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}-\frac{\cos \left(a+b \log \left(c x^n\right)\right)}{b n}","\frac{\cos ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}-\frac{\cos \left(a+b \log \left(c x^n\right)\right)}{b n}",1,"-(Cos[a + b*Log[c*x^n]]/(b*n)) + Cos[a + b*Log[c*x^n]]^3/(3*b*n)","A",3,1,17,0.05882,1,"{2633}"
17,1,158,0,0.0468833,"\int \frac{\sin ^3\left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[Sin[a + b*Log[c*x^n]]^3/x^2,x]","-\frac{\sin ^3\left(a+b \log \left(c x^n\right)\right)}{x \left(9 b^2 n^2+1\right)}-\frac{6 b^2 n^2 \sin \left(a+b \log \left(c x^n\right)\right)}{x \left(9 b^4 n^4+10 b^2 n^2+1\right)}-\frac{6 b^3 n^3 \cos \left(a+b \log \left(c x^n\right)\right)}{x \left(9 b^4 n^4+10 b^2 n^2+1\right)}-\frac{3 b n \sin ^2\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{x \left(9 b^2 n^2+1\right)}","-\frac{\sin ^3\left(a+b \log \left(c x^n\right)\right)}{x \left(9 b^2 n^2+1\right)}-\frac{6 b^2 n^2 \sin \left(a+b \log \left(c x^n\right)\right)}{x \left(9 b^4 n^4+10 b^2 n^2+1\right)}-\frac{6 b^3 n^3 \cos \left(a+b \log \left(c x^n\right)\right)}{x \left(9 b^4 n^4+10 b^2 n^2+1\right)}-\frac{3 b n \sin ^2\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{x \left(9 b^2 n^2+1\right)}",1,"(-6*b^3*n^3*Cos[a + b*Log[c*x^n]])/((1 + 10*b^2*n^2 + 9*b^4*n^4)*x) - (6*b^2*n^2*Sin[a + b*Log[c*x^n]])/((1 + 10*b^2*n^2 + 9*b^4*n^4)*x) - (3*b*n*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]]^2)/((1 + 9*b^2*n^2)*x) - Sin[a + b*Log[c*x^n]]^3/((1 + 9*b^2*n^2)*x)","A",2,2,17,0.1176,1,"{4487, 4485}"
18,1,158,0,0.0477091,"\int \frac{\sin ^3\left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[Sin[a + b*Log[c*x^n]]^3/x^3,x]","-\frac{2 \sin ^3\left(a+b \log \left(c x^n\right)\right)}{x^2 \left(9 b^2 n^2+4\right)}-\frac{12 b^2 n^2 \sin \left(a+b \log \left(c x^n\right)\right)}{x^2 \left(9 b^4 n^4+40 b^2 n^2+16\right)}-\frac{6 b^3 n^3 \cos \left(a+b \log \left(c x^n\right)\right)}{x^2 \left(9 b^4 n^4+40 b^2 n^2+16\right)}-\frac{3 b n \sin ^2\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{x^2 \left(9 b^2 n^2+4\right)}","-\frac{2 \sin ^3\left(a+b \log \left(c x^n\right)\right)}{x^2 \left(9 b^2 n^2+4\right)}-\frac{12 b^2 n^2 \sin \left(a+b \log \left(c x^n\right)\right)}{x^2 \left(9 b^4 n^4+40 b^2 n^2+16\right)}-\frac{6 b^3 n^3 \cos \left(a+b \log \left(c x^n\right)\right)}{x^2 \left(9 b^4 n^4+40 b^2 n^2+16\right)}-\frac{3 b n \sin ^2\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{x^2 \left(9 b^2 n^2+4\right)}",1,"(-6*b^3*n^3*Cos[a + b*Log[c*x^n]])/((16 + 40*b^2*n^2 + 9*b^4*n^4)*x^2) - (12*b^2*n^2*Sin[a + b*Log[c*x^n]])/((16 + 40*b^2*n^2 + 9*b^4*n^4)*x^2) - (3*b*n*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]]^2)/((4 + 9*b^2*n^2)*x^2) - (2*Sin[a + b*Log[c*x^n]]^3)/((4 + 9*b^2*n^2)*x^2)","A",2,2,17,0.1176,1,"{4487, 4485}"
19,1,202,0,0.0783835,"\int x^2 \sin ^4\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*Sin[a + b*Log[c*x^n]]^4,x]","\frac{36 b^2 n^2 x^3 \sin ^2\left(a+b \log \left(c x^n\right)\right)}{64 b^4 n^4+180 b^2 n^2+81}+\frac{3 x^3 \sin ^4\left(a+b \log \left(c x^n\right)\right)}{16 b^2 n^2+9}-\frac{4 b n x^3 \sin ^3\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{16 b^2 n^2+9}-\frac{24 b^3 n^3 x^3 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{64 b^4 n^4+180 b^2 n^2+81}+\frac{8 b^4 n^4 x^3}{64 b^4 n^4+180 b^2 n^2+81}","\frac{36 b^2 n^2 x^3 \sin ^2\left(a+b \log \left(c x^n\right)\right)}{64 b^4 n^4+180 b^2 n^2+81}+\frac{3 x^3 \sin ^4\left(a+b \log \left(c x^n\right)\right)}{16 b^2 n^2+9}-\frac{4 b n x^3 \sin ^3\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{16 b^2 n^2+9}-\frac{24 b^3 n^3 x^3 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{64 b^4 n^4+180 b^2 n^2+81}+\frac{8 b^4 n^4 x^3}{64 b^4 n^4+180 b^2 n^2+81}",1,"(8*b^4*n^4*x^3)/(81 + 180*b^2*n^2 + 64*b^4*n^4) - (24*b^3*n^3*x^3*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/(81 + 180*b^2*n^2 + 64*b^4*n^4) + (36*b^2*n^2*x^3*Sin[a + b*Log[c*x^n]]^2)/(81 + 180*b^2*n^2 + 64*b^4*n^4) - (4*b*n*x^3*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]]^3)/(9 + 16*b^2*n^2) + (3*x^3*Sin[a + b*Log[c*x^n]]^4)/(9 + 16*b^2*n^2)","A",3,2,17,0.1176,1,"{4487, 30}"
20,1,210,0,0.0609191,"\int x \sin ^4\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Sin[a + b*Log[c*x^n]]^4,x]","\frac{3 b^2 n^2 x^2 \sin ^2\left(a+b \log \left(c x^n\right)\right)}{2 \left(4 b^4 n^4+5 b^2 n^2+1\right)}+\frac{x^2 \sin ^4\left(a+b \log \left(c x^n\right)\right)}{2 \left(4 b^2 n^2+1\right)}-\frac{b n x^2 \sin ^3\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+1}-\frac{3 b^3 n^3 x^2 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{2 \left(4 b^4 n^4+5 b^2 n^2+1\right)}+\frac{3 b^4 n^4 x^2}{4 \left(4 b^4 n^4+5 b^2 n^2+1\right)}","\frac{3 b^2 n^2 x^2 \sin ^2\left(a+b \log \left(c x^n\right)\right)}{2 \left(4 b^4 n^4+5 b^2 n^2+1\right)}+\frac{x^2 \sin ^4\left(a+b \log \left(c x^n\right)\right)}{2 \left(4 b^2 n^2+1\right)}-\frac{b n x^2 \sin ^3\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+1}-\frac{3 b^3 n^3 x^2 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{2 \left(4 b^4 n^4+5 b^2 n^2+1\right)}+\frac{3 b^4 n^4 x^2}{4 \left(4 b^4 n^4+5 b^2 n^2+1\right)}",1,"(3*b^4*n^4*x^2)/(4*(1 + 5*b^2*n^2 + 4*b^4*n^4)) - (3*b^3*n^3*x^2*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/(2*(1 + 5*b^2*n^2 + 4*b^4*n^4)) + (3*b^2*n^2*x^2*Sin[a + b*Log[c*x^n]]^2)/(2*(1 + 5*b^2*n^2 + 4*b^4*n^4)) - (b*n*x^2*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]]^3)/(1 + 4*b^2*n^2) + (x^2*Sin[a + b*Log[c*x^n]]^4)/(2*(1 + 4*b^2*n^2))","A",3,2,15,0.1333,1,"{4487, 30}"
21,1,191,0,0.0511131,"\int \sin ^4\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sin[a + b*Log[c*x^n]]^4,x]","\frac{12 b^2 n^2 x \sin ^2\left(a+b \log \left(c x^n\right)\right)}{64 b^4 n^4+20 b^2 n^2+1}+\frac{x \sin ^4\left(a+b \log \left(c x^n\right)\right)}{16 b^2 n^2+1}-\frac{4 b n x \sin ^3\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{16 b^2 n^2+1}-\frac{24 b^3 n^3 x \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{64 b^4 n^4+20 b^2 n^2+1}+\frac{24 b^4 n^4 x}{64 b^4 n^4+20 b^2 n^2+1}","\frac{12 b^2 n^2 x \sin ^2\left(a+b \log \left(c x^n\right)\right)}{64 b^4 n^4+20 b^2 n^2+1}+\frac{x \sin ^4\left(a+b \log \left(c x^n\right)\right)}{16 b^2 n^2+1}-\frac{4 b n x \sin ^3\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{16 b^2 n^2+1}-\frac{24 b^3 n^3 x \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{64 b^4 n^4+20 b^2 n^2+1}+\frac{24 b^4 n^4 x}{64 b^4 n^4+20 b^2 n^2+1}",1,"(24*b^4*n^4*x)/(1 + 20*b^2*n^2 + 64*b^4*n^4) - (24*b^3*n^3*x*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/(1 + 20*b^2*n^2 + 64*b^4*n^4) + (12*b^2*n^2*x*Sin[a + b*Log[c*x^n]]^2)/(1 + 20*b^2*n^2 + 64*b^4*n^4) - (4*b*n*x*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]]^3)/(1 + 16*b^2*n^2) + (x*Sin[a + b*Log[c*x^n]]^4)/(1 + 16*b^2*n^2)","A",3,2,13,0.1538,1,"{4477, 8}"
22,1,73,0,0.0494805,"\int \frac{\sin ^4\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Sin[a + b*Log[c*x^n]]^4/x,x]","-\frac{\sin ^3\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{4 b n}-\frac{3 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{8 b n}+\frac{3 \log (x)}{8}","-\frac{\sin ^3\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{4 b n}-\frac{3 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{8 b n}+\frac{3 \log (x)}{8}",1,"(3*Log[x])/8 - (3*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/(8*b*n) - (Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]]^3)/(4*b*n)","A",4,2,17,0.1176,1,"{2635, 8}"
23,1,202,0,0.0656843,"\int \frac{\sin ^4\left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[Sin[a + b*Log[c*x^n]]^4/x^2,x]","-\frac{12 b^2 n^2 \sin ^2\left(a+b \log \left(c x^n\right)\right)}{x \left(64 b^4 n^4+20 b^2 n^2+1\right)}-\frac{\sin ^4\left(a+b \log \left(c x^n\right)\right)}{x \left(16 b^2 n^2+1\right)}-\frac{4 b n \sin ^3\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{x \left(16 b^2 n^2+1\right)}-\frac{24 b^3 n^3 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{x \left(64 b^4 n^4+20 b^2 n^2+1\right)}-\frac{24 b^4 n^4}{x \left(64 b^4 n^4+20 b^2 n^2+1\right)}","-\frac{12 b^2 n^2 \sin ^2\left(a+b \log \left(c x^n\right)\right)}{x \left(64 b^4 n^4+20 b^2 n^2+1\right)}-\frac{\sin ^4\left(a+b \log \left(c x^n\right)\right)}{x \left(16 b^2 n^2+1\right)}-\frac{4 b n \sin ^3\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{x \left(16 b^2 n^2+1\right)}-\frac{24 b^3 n^3 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{x \left(64 b^4 n^4+20 b^2 n^2+1\right)}-\frac{24 b^4 n^4}{x \left(64 b^4 n^4+20 b^2 n^2+1\right)}",1,"(-24*b^4*n^4)/((1 + 20*b^2*n^2 + 64*b^4*n^4)*x) - (24*b^3*n^3*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/((1 + 20*b^2*n^2 + 64*b^4*n^4)*x) - (12*b^2*n^2*Sin[a + b*Log[c*x^n]]^2)/((1 + 20*b^2*n^2 + 64*b^4*n^4)*x) - (4*b*n*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]]^3)/((1 + 16*b^2*n^2)*x) - Sin[a + b*Log[c*x^n]]^4/((1 + 16*b^2*n^2)*x)","A",3,2,17,0.1176,1,"{4487, 30}"
24,1,210,0,0.0628864,"\int \frac{\sin ^4\left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[Sin[a + b*Log[c*x^n]]^4/x^3,x]","-\frac{3 b^2 n^2 \sin ^2\left(a+b \log \left(c x^n\right)\right)}{2 x^2 \left(4 b^4 n^4+5 b^2 n^2+1\right)}-\frac{\sin ^4\left(a+b \log \left(c x^n\right)\right)}{2 x^2 \left(4 b^2 n^2+1\right)}-\frac{b n \sin ^3\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{x^2 \left(4 b^2 n^2+1\right)}-\frac{3 b^3 n^3 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{2 x^2 \left(4 b^4 n^4+5 b^2 n^2+1\right)}-\frac{3 b^4 n^4}{4 x^2 \left(4 b^4 n^4+5 b^2 n^2+1\right)}","-\frac{3 b^2 n^2 \sin ^2\left(a+b \log \left(c x^n\right)\right)}{2 x^2 \left(4 b^4 n^4+5 b^2 n^2+1\right)}-\frac{\sin ^4\left(a+b \log \left(c x^n\right)\right)}{2 x^2 \left(4 b^2 n^2+1\right)}-\frac{b n \sin ^3\left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{x^2 \left(4 b^2 n^2+1\right)}-\frac{3 b^3 n^3 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{2 x^2 \left(4 b^4 n^4+5 b^2 n^2+1\right)}-\frac{3 b^4 n^4}{4 x^2 \left(4 b^4 n^4+5 b^2 n^2+1\right)}",1,"(-3*b^4*n^4)/(4*(1 + 5*b^2*n^2 + 4*b^4*n^4)*x^2) - (3*b^3*n^3*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/(2*(1 + 5*b^2*n^2 + 4*b^4*n^4)*x^2) - (3*b^2*n^2*Sin[a + b*Log[c*x^n]]^2)/(2*(1 + 5*b^2*n^2 + 4*b^4*n^4)*x^2) - (b*n*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]]^3)/((1 + 4*b^2*n^2)*x^2) - Sin[a + b*Log[c*x^n]]^4/(2*(1 + 4*b^2*n^2)*x^2)","A",3,2,17,0.1176,1,"{4487, 30}"
25,1,39,0,0.0142934,"\int \sin (\log (a+b x)) \, dx","Int[Sin[Log[a + b*x]],x]","\frac{(a+b x) \sin (\log (a+b x))}{2 b}-\frac{(a+b x) \cos (\log (a+b x))}{2 b}","\frac{(a+b x) \sin (\log (a+b x))}{2 b}-\frac{(a+b x) \cos (\log (a+b x))}{2 b}",1,"-((a + b*x)*Cos[Log[a + b*x]])/(2*b) + ((a + b*x)*Sin[Log[a + b*x]])/(2*b)","A",2,1,7,0.1429,1,"{4475}"
26,1,133,0,0.2773585,"\int x^m \sin \left(a+\sqrt{-\frac{(1+m)^2}{n^2}} \log \left(c x^n\right)\right) \, dx","Int[x^m*Sin[a + Sqrt[-((1 + m)^2/n^2)]*Log[c*x^n]],x]","\frac{(m+1) x^{m+1} \log (x) e^{\frac{a n \sqrt{-\frac{(m+1)^2}{n^2}}}{m+1}} \left(c x^n\right)^{-\frac{m+1}{n}}}{2 n \sqrt{-\frac{(m+1)^2}{n^2}}}-\frac{x^{m+1} e^{\frac{a (m+1)}{n \sqrt{-\frac{(m+1)^2}{n^2}}}} \left(c x^n\right)^{\frac{m+1}{n}}}{4 n \sqrt{-\frac{(m+1)^2}{n^2}}}","\frac{(m+1) x^{m+1} \log (x) e^{\frac{a n \sqrt{-\frac{(m+1)^2}{n^2}}}{m+1}} \left(c x^n\right)^{-\frac{m+1}{n}}}{2 n \sqrt{-\frac{(m+1)^2}{n^2}}}-\frac{x^{m+1} e^{\frac{a (m+1)}{n \sqrt{-\frac{(m+1)^2}{n^2}}}} \left(c x^n\right)^{\frac{m+1}{n}}}{4 n \sqrt{-\frac{(m+1)^2}{n^2}}}",1,"-(E^((a*(1 + m))/(Sqrt[-((1 + m)^2/n^2)]*n))*x^(1 + m)*(c*x^n)^((1 + m)/n))/(4*Sqrt[-((1 + m)^2/n^2)]*n) + (E^((a*Sqrt[-((1 + m)^2/n^2)]*n)/(1 + m))*(1 + m)*x^(1 + m)*Log[x])/(2*Sqrt[-((1 + m)^2/n^2)]*n*(c*x^n)^((1 + m)/n))","A",3,2,28,0.07143,1,"{4493, 4489}"
27,1,88,0,0.0988647,"\int x^2 \sin \left(a+3 \sqrt{-\frac{1}{n^2}} \log \left(c x^n\right)\right) \, dx","Int[x^2*Sin[a + 3*Sqrt[-n^(-2)]*Log[c*x^n]],x]","\frac{1}{12} \sqrt{-\frac{1}{n^2}} n x^3 e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{3/n}-\frac{1}{2} \sqrt{-\frac{1}{n^2}} n x^3 e^{a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-3/n}","\frac{1}{12} \sqrt{-\frac{1}{n^2}} n x^3 e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{3/n}-\frac{1}{2} \sqrt{-\frac{1}{n^2}} n x^3 e^{a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-3/n}",1,"(Sqrt[-n^(-2)]*n*x^3*(c*x^n)^(3/n))/(12*E^(a*Sqrt[-n^(-2)]*n)) - (E^(a*Sqrt[-n^(-2)]*n)*Sqrt[-n^(-2)]*n*x^3*Log[x])/(2*(c*x^n)^(3/n))","A",3,2,24,0.08333,1,"{4493, 4489}"
28,1,88,0,0.0518887,"\int x \sin \left(a+2 \sqrt{-\frac{1}{n^2}} \log \left(c x^n\right)\right) \, dx","Int[x*Sin[a + 2*Sqrt[-n^(-2)]*Log[c*x^n]],x]","\frac{1}{8} \sqrt{-\frac{1}{n^2}} n x^2 e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{2/n}-\frac{1}{2} \sqrt{-\frac{1}{n^2}} n x^2 e^{a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-2/n}","\frac{1}{8} \sqrt{-\frac{1}{n^2}} n x^2 e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{2/n}-\frac{1}{2} \sqrt{-\frac{1}{n^2}} n x^2 e^{a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-2/n}",1,"(Sqrt[-n^(-2)]*n*x^2*(c*x^n)^(2/n))/(8*E^(a*Sqrt[-n^(-2)]*n)) - (E^(a*Sqrt[-n^(-2)]*n)*Sqrt[-n^(-2)]*n*x^2*Log[x])/(2*(c*x^n)^(2/n))","A",3,2,22,0.09091,1,"{4493, 4489}"
29,1,82,0,0.0517531,"\int \sin \left(a+\sqrt{-\frac{1}{n^2}} \log \left(c x^n\right)\right) \, dx","Int[Sin[a + Sqrt[-n^(-2)]*Log[c*x^n]],x]","\frac{1}{4} \sqrt{-\frac{1}{n^2}} n x e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\frac{1}{n}}-\frac{1}{2} \sqrt{-\frac{1}{n^2}} n x e^{a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-1/n}","\frac{1}{4} \sqrt{-\frac{1}{n^2}} n x e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\frac{1}{n}}-\frac{1}{2} \sqrt{-\frac{1}{n^2}} n x e^{a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-1/n}",1,"(Sqrt[-n^(-2)]*n*x*(c*x^n)^n^(-1))/(4*E^(a*Sqrt[-n^(-2)]*n)) - (E^(a*Sqrt[-n^(-2)]*n)*Sqrt[-n^(-2)]*n*x*Log[x])/(2*(c*x^n)^n^(-1))","A",3,2,19,0.1053,1,"{4483, 4489}"
30,1,5,0,0.0044641,"\int \frac{\sin (a)}{x} \, dx","Int[Sin[a]/x,x]","\sin (a) \log (x)","\sin (a) \log (x)",1,"Log[x]*Sin[a]","A",2,2,6,0.3333,1,"{12, 29}"
31,1,86,0,0.0611679,"\int \frac{\sin \left(a+\sqrt{-\frac{1}{n^2}} \log \left(c x^n\right)\right)}{x^2} \, dx","Int[Sin[a + Sqrt[-n^(-2)]*Log[c*x^n]]/x^2,x]","\frac{\sqrt{-\frac{1}{n^2}} n e^{a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{-1/n}}{4 x}+\frac{\sqrt{-\frac{1}{n^2}} n e^{-a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{\frac{1}{n}}}{2 x}","\frac{\sqrt{-\frac{1}{n^2}} n e^{a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{-1/n}}{4 x}+\frac{\sqrt{-\frac{1}{n^2}} n e^{-a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{\frac{1}{n}}}{2 x}",1,"(E^(a*Sqrt[-n^(-2)]*n)*Sqrt[-n^(-2)]*n)/(4*x*(c*x^n)^n^(-1)) + (Sqrt[-n^(-2)]*n*(c*x^n)^n^(-1)*Log[x])/(2*E^(a*Sqrt[-n^(-2)]*n)*x)","A",3,2,23,0.08696,1,"{4493, 4489}"
32,1,88,0,0.0531861,"\int \frac{\sin \left(a+2 \sqrt{-\frac{1}{n^2}} \log \left(c x^n\right)\right)}{x^3} \, dx","Int[Sin[a + 2*Sqrt[-n^(-2)]*Log[c*x^n]]/x^3,x]","\frac{\sqrt{-\frac{1}{n^2}} n e^{a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{-2/n}}{8 x^2}+\frac{\sqrt{-\frac{1}{n^2}} n e^{-a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{2/n}}{2 x^2}","\frac{\sqrt{-\frac{1}{n^2}} n e^{a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{-2/n}}{8 x^2}+\frac{\sqrt{-\frac{1}{n^2}} n e^{-a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{2/n}}{2 x^2}",1,"(E^(a*Sqrt[-n^(-2)]*n)*Sqrt[-n^(-2)]*n)/(8*x^2*(c*x^n)^(2/n)) + (Sqrt[-n^(-2)]*n*(c*x^n)^(2/n)*Log[x])/(2*E^(a*Sqrt[-n^(-2)]*n)*x^2)","A",3,2,24,0.08333,1,"{4493, 4489}"
33,1,117,0,0.1588499,"\int x^m \sin ^2\left(a+\frac{1}{2} \sqrt{-\frac{(1+m)^2}{n^2}} \log \left(c x^n\right)\right) \, dx","Int[x^m*Sin[a + (Sqrt[-((1 + m)^2/n^2)]*Log[c*x^n])/2]^2,x]","-\frac{x^{m+1} e^{-\frac{2 a n \sqrt{-\frac{(m+1)^2}{n^2}}}{m+1}} \left(c x^n\right)^{\frac{m+1}{n}}}{8 (m+1)}-\frac{1}{4} x^{m+1} \log (x) e^{\frac{2 a n \sqrt{-\frac{(m+1)^2}{n^2}}}{m+1}} \left(c x^n\right)^{-\frac{m+1}{n}}+\frac{x^{m+1}}{2 (m+1)}","-\frac{x^{m+1} e^{-\frac{2 a n \sqrt{-\frac{(m+1)^2}{n^2}}}{m+1}} \left(c x^n\right)^{\frac{m+1}{n}}}{8 (m+1)}-\frac{1}{4} x^{m+1} \log (x) e^{\frac{2 a n \sqrt{-\frac{(m+1)^2}{n^2}}}{m+1}} \left(c x^n\right)^{-\frac{m+1}{n}}+\frac{x^{m+1}}{2 (m+1)}",1,"x^(1 + m)/(2*(1 + m)) - (x^(1 + m)*(c*x^n)^((1 + m)/n))/(8*E^((2*a*Sqrt[-((1 + m)^2/n^2)]*n)/(1 + m))*(1 + m)) - (E^((2*a*Sqrt[-((1 + m)^2/n^2)]*n)/(1 + m))*x^(1 + m)*Log[x])/(4*(c*x^n)^((1 + m)/n))","A",3,2,33,0.06061,1,"{4493, 4489}"
34,1,76,0,0.0755471,"\int x^2 \sin ^2\left(a+\frac{3}{2} \sqrt{-\frac{1}{n^2}} \log \left(c x^n\right)\right) \, dx","Int[x^2*Sin[a + (3*Sqrt[-n^(-2)]*Log[c*x^n])/2]^2,x]","-\frac{1}{24} x^3 e^{-2 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{3/n}-\frac{1}{4} x^3 e^{2 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-3/n}+\frac{x^3}{6}","-\frac{1}{24} x^3 e^{-2 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{3/n}-\frac{1}{4} x^3 e^{2 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-3/n}+\frac{x^3}{6}",1,"x^3/6 - (x^3*(c*x^n)^(3/n))/(24*E^(2*a*Sqrt[-n^(-2)]*n)) - (E^(2*a*Sqrt[-n^(-2)]*n)*x^3*Log[x])/(4*(c*x^n)^(3/n))","A",3,2,28,0.07143,1,"{4493, 4489}"
35,1,76,0,0.05761,"\int x \sin ^2\left(a+\sqrt{-\frac{1}{n^2}} \log \left(c x^n\right)\right) \, dx","Int[x*Sin[a + Sqrt[-n^(-2)]*Log[c*x^n]]^2,x]","-\frac{1}{16} x^2 e^{-2 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{2/n}-\frac{1}{4} x^2 e^{2 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-2/n}+\frac{x^2}{4}","-\frac{1}{16} x^2 e^{-2 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{2/n}-\frac{1}{4} x^2 e^{2 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-2/n}+\frac{x^2}{4}",1,"x^2/4 - (x^2*(c*x^n)^(2/n))/(16*E^(2*a*Sqrt[-n^(-2)]*n)) - (E^(2*a*Sqrt[-n^(-2)]*n)*x^2*Log[x])/(4*(c*x^n)^(2/n))","A",3,2,23,0.08696,1,"{4493, 4489}"
36,1,68,0,0.0549811,"\int \sin ^2\left(a+\frac{1}{2} \sqrt{-\frac{1}{n^2}} \log \left(c x^n\right)\right) \, dx","Int[Sin[a + (Sqrt[-n^(-2)]*Log[c*x^n])/2]^2,x]","-\frac{1}{8} x e^{-2 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\frac{1}{n}}-\frac{1}{4} x e^{2 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-1/n}+\frac{x}{2}","-\frac{1}{8} x e^{-2 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\frac{1}{n}}-\frac{1}{4} x e^{2 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-1/n}+\frac{x}{2}",1,"x/2 - (x*(c*x^n)^n^(-1))/(8*E^(2*a*Sqrt[-n^(-2)]*n)) - (E^(2*a*Sqrt[-n^(-2)]*n)*x*Log[x])/(4*(c*x^n)^n^(-1))","A",3,2,24,0.08333,1,"{4483, 4489}"
37,1,7,0,0.006046,"\int \frac{\sin ^2(a)}{x} \, dx","Int[Sin[a]^2/x,x]","\sin ^2(a) \log (x)","\sin ^2(a) \log (x)",1,"Log[x]*Sin[a]^2","A",2,2,8,0.2500,1,"{12, 29}"
38,1,74,0,0.068497,"\int \frac{\sin ^2\left(a+\frac{1}{2} \sqrt{-\frac{1}{n^2}} \log \left(c x^n\right)\right)}{x^2} \, dx","Int[Sin[a + (Sqrt[-n^(-2)]*Log[c*x^n])/2]^2/x^2,x]","\frac{e^{2 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{-1/n}}{8 x}-\frac{e^{-2 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{\frac{1}{n}}}{4 x}-\frac{1}{2 x}","\frac{e^{2 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{-1/n}}{8 x}-\frac{e^{-2 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{\frac{1}{n}}}{4 x}-\frac{1}{2 x}",1,"-1/(2*x) + E^(2*a*Sqrt[-n^(-2)]*n)/(8*x*(c*x^n)^n^(-1)) - ((c*x^n)^n^(-1)*Log[x])/(4*E^(2*a*Sqrt[-n^(-2)]*n)*x)","A",3,2,28,0.07143,1,"{4493, 4489}"
39,1,76,0,0.06197,"\int \frac{\sin ^2\left(a+\sqrt{-\frac{1}{n^2}} \log \left(c x^n\right)\right)}{x^3} \, dx","Int[Sin[a + Sqrt[-n^(-2)]*Log[c*x^n]]^2/x^3,x]","\frac{e^{2 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{-2/n}}{16 x^2}-\frac{e^{-2 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{2/n}}{4 x^2}-\frac{1}{4 x^2}","\frac{e^{2 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{-2/n}}{16 x^2}-\frac{e^{-2 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{2/n}}{4 x^2}-\frac{1}{4 x^2}",1,"-1/(4*x^2) + E^(2*a*Sqrt[-n^(-2)]*n)/(16*x^2*(c*x^n)^(2/n)) - ((c*x^n)^(2/n)*Log[x])/(4*E^(2*a*Sqrt[-n^(-2)]*n)*x^2)","A",3,2,25,0.08000,1,"{4493, 4489}"
40,1,226,0,0.0790366,"\int x^m \sin ^3\left(a+\frac{1}{2} \sqrt{-\frac{(1+m)^2}{n^2}} \log \left(c x^n\right)\right) \, dx","Int[x^m*Sin[a + (Sqrt[-((1 + m)^2/n^2)]*Log[c*x^n])/2]^3,x]","-\frac{4 x^{m+1} \sin ^3\left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right)}{5 (m+1)}+\frac{8 x^{m+1} \sin \left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right)}{5 (m+1)}-\frac{4 n \sqrt{-\frac{(m+1)^2}{n^2}} x^{m+1} \cos \left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right)}{5 (m+1)^2}+\frac{6 n \sqrt{-\frac{(m+1)^2}{n^2}} x^{m+1} \sin ^2\left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right) \cos \left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right)}{5 (m+1)^2}","-\frac{4 x^{m+1} \sin ^3\left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right)}{5 (m+1)}+\frac{8 x^{m+1} \sin \left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right)}{5 (m+1)}-\frac{4 n \sqrt{-\frac{(m+1)^2}{n^2}} x^{m+1} \cos \left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right)}{5 (m+1)^2}+\frac{6 n \sqrt{-\frac{(m+1)^2}{n^2}} x^{m+1} \sin ^2\left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right) \cos \left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right)}{5 (m+1)^2}",1,"(-4*Sqrt[-((1 + m)^2/n^2)]*n*x^(1 + m)*Cos[a + (Sqrt[-((1 + m)^2/n^2)]*Log[c*x^n])/2])/(5*(1 + m)^2) + (8*x^(1 + m)*Sin[a + (Sqrt[-((1 + m)^2/n^2)]*Log[c*x^n])/2])/(5*(1 + m)) + (6*Sqrt[-((1 + m)^2/n^2)]*n*x^(1 + m)*Cos[a + (Sqrt[-((1 + m)^2/n^2)]*Log[c*x^n])/2]*Sin[a + (Sqrt[-((1 + m)^2/n^2)]*Log[c*x^n])/2]^2)/(5*(1 + m)^2) - (4*x^(1 + m)*Sin[a + (Sqrt[-((1 + m)^2/n^2)]*Log[c*x^n])/2]^3)/(5*(1 + m))","A",2,2,33,0.06061,1,"{4487, 4485}"
41,1,172,0,0.1605944,"\int x^2 \sin ^3\left(a+\sqrt{-\frac{1}{n^2}} \log \left(c x^n\right)\right) \, dx","Int[x^2*Sin[a + Sqrt[-n^(-2)]*Log[c*x^n]]^3,x]","-\frac{3}{16} \sqrt{-\frac{1}{n^2}} n x^3 e^{a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{-1/n}-\frac{1}{48} \sqrt{-\frac{1}{n^2}} n x^3 e^{-3 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{3/n}+\frac{3}{32} \sqrt{-\frac{1}{n^2}} n x^3 e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\frac{1}{n}}+\frac{1}{8} \sqrt{-\frac{1}{n^2}} n x^3 e^{3 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-3/n}","-\frac{3}{16} \sqrt{-\frac{1}{n^2}} n x^3 e^{a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{-1/n}-\frac{1}{48} \sqrt{-\frac{1}{n^2}} n x^3 e^{-3 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{3/n}+\frac{3}{32} \sqrt{-\frac{1}{n^2}} n x^3 e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\frac{1}{n}}+\frac{1}{8} \sqrt{-\frac{1}{n^2}} n x^3 e^{3 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-3/n}",1,"(-3*E^(a*Sqrt[-n^(-2)]*n)*Sqrt[-n^(-2)]*n*x^3)/(16*(c*x^n)^n^(-1)) + (3*Sqrt[-n^(-2)]*n*x^3*(c*x^n)^n^(-1))/(32*E^(a*Sqrt[-n^(-2)]*n)) - (Sqrt[-n^(-2)]*n*x^3*(c*x^n)^(3/n))/(48*E^(3*a*Sqrt[-n^(-2)]*n)) + (E^(3*a*Sqrt[-n^(-2)]*n)*Sqrt[-n^(-2)]*n*x^3*Log[x])/(8*(c*x^n)^(3/n))","A",3,2,25,0.08000,1,"{4493, 4489}"
42,1,178,0,0.1109026,"\int x \sin ^3\left(a+\frac{2}{3} \sqrt{-\frac{1}{n^2}} \log \left(c x^n\right)\right) \, dx","Int[x*Sin[a + (2*Sqrt[-n^(-2)]*Log[c*x^n])/3]^3,x]","-\frac{9}{32} \sqrt{-\frac{1}{n^2}} n x^2 e^{a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.-\frac{2}{3}\right/n}+\frac{9}{64} \sqrt{-\frac{1}{n^2}} n x^2 e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.\frac{2}{3}\right/n}-\frac{1}{32} \sqrt{-\frac{1}{n^2}} n x^2 e^{-3 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{2/n}+\frac{1}{8} \sqrt{-\frac{1}{n^2}} n x^2 e^{3 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-2/n}","-\frac{9}{32} \sqrt{-\frac{1}{n^2}} n x^2 e^{a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.-\frac{2}{3}\right/n}+\frac{9}{64} \sqrt{-\frac{1}{n^2}} n x^2 e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.\frac{2}{3}\right/n}-\frac{1}{32} \sqrt{-\frac{1}{n^2}} n x^2 e^{-3 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{2/n}+\frac{1}{8} \sqrt{-\frac{1}{n^2}} n x^2 e^{3 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-2/n}",1,"(-9*E^(a*Sqrt[-n^(-2)]*n)*Sqrt[-n^(-2)]*n*x^2)/(32*(c*x^n)^(2/(3*n))) + (9*Sqrt[-n^(-2)]*n*x^2*(c*x^n)^(2/(3*n)))/(64*E^(a*Sqrt[-n^(-2)]*n)) - (Sqrt[-n^(-2)]*n*x^2*(c*x^n)^(2/n))/(32*E^(3*a*Sqrt[-n^(-2)]*n)) + (E^(3*a*Sqrt[-n^(-2)]*n)*Sqrt[-n^(-2)]*n*x^2*Log[x])/(8*(c*x^n)^(2/n))","A",3,2,26,0.07692,1,"{4493, 4489}"
43,1,168,0,0.1049307,"\int \sin ^3\left(a+\frac{1}{3} \sqrt{-\frac{1}{n^2}} \log \left(c x^n\right)\right) \, dx","Int[Sin[a + (Sqrt[-n^(-2)]*Log[c*x^n])/3]^3,x]","-\frac{9}{16} \sqrt{-\frac{1}{n^2}} n x e^{a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.-\frac{1}{3}\right/n}+\frac{9}{32} \sqrt{-\frac{1}{n^2}} n x e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.\frac{1}{3}\right/n}-\frac{1}{16} \sqrt{-\frac{1}{n^2}} n x e^{-3 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\frac{1}{n}}+\frac{1}{8} \sqrt{-\frac{1}{n^2}} n x e^{3 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-1/n}","-\frac{9}{16} \sqrt{-\frac{1}{n^2}} n x e^{a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.-\frac{1}{3}\right/n}+\frac{9}{32} \sqrt{-\frac{1}{n^2}} n x e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.\frac{1}{3}\right/n}-\frac{1}{16} \sqrt{-\frac{1}{n^2}} n x e^{-3 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\frac{1}{n}}+\frac{1}{8} \sqrt{-\frac{1}{n^2}} n x e^{3 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-1/n}",1,"(-9*E^(a*Sqrt[-n^(-2)]*n)*Sqrt[-n^(-2)]*n*x)/(16*(c*x^n)^(1/(3*n))) + (9*Sqrt[-n^(-2)]*n*x*(c*x^n)^(1/(3*n)))/(32*E^(a*Sqrt[-n^(-2)]*n)) - (Sqrt[-n^(-2)]*n*x*(c*x^n)^n^(-1))/(16*E^(3*a*Sqrt[-n^(-2)]*n)) + (E^(3*a*Sqrt[-n^(-2)]*n)*Sqrt[-n^(-2)]*n*x*Log[x])/(8*(c*x^n)^n^(-1))","A",3,2,24,0.08333,1,"{4483, 4489}"
44,1,7,0,0.0047063,"\int \frac{\sin ^3(a)}{x} \, dx","Int[Sin[a]^3/x,x]","\sin ^3(a) \log (x)","\sin ^3(a) \log (x)",1,"Log[x]*Sin[a]^3","A",2,2,8,0.2500,1,"{12, 29}"
45,1,176,0,0.1317598,"\int \frac{\sin ^3\left(a+\frac{1}{3} \sqrt{-\frac{1}{n^2}} \log \left(c x^n\right)\right)}{x^2} \, dx","Int[Sin[a + (Sqrt[-n^(-2)]*Log[c*x^n])/3]^3/x^2,x]","-\frac{\sqrt{-\frac{1}{n^2}} n e^{3 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{-1/n}}{16 x}+\frac{9 \sqrt{-\frac{1}{n^2}} n e^{a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.-\frac{1}{3}\right/n}}{32 x}-\frac{9 \sqrt{-\frac{1}{n^2}} n e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.\frac{1}{3}\right/n}}{16 x}-\frac{\sqrt{-\frac{1}{n^2}} n e^{-3 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{\frac{1}{n}}}{8 x}","-\frac{\sqrt{-\frac{1}{n^2}} n e^{3 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{-1/n}}{16 x}+\frac{9 \sqrt{-\frac{1}{n^2}} n e^{a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.-\frac{1}{3}\right/n}}{32 x}-\frac{9 \sqrt{-\frac{1}{n^2}} n e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.\frac{1}{3}\right/n}}{16 x}-\frac{\sqrt{-\frac{1}{n^2}} n e^{-3 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{\frac{1}{n}}}{8 x}",1,"-(E^(3*a*Sqrt[-n^(-2)]*n)*Sqrt[-n^(-2)]*n)/(16*x*(c*x^n)^n^(-1)) + (9*E^(a*Sqrt[-n^(-2)]*n)*Sqrt[-n^(-2)]*n)/(32*x*(c*x^n)^(1/(3*n))) - (9*Sqrt[-n^(-2)]*n*(c*x^n)^(1/(3*n)))/(16*E^(a*Sqrt[-n^(-2)]*n)*x) - (Sqrt[-n^(-2)]*n*(c*x^n)^n^(-1)*Log[x])/(8*E^(3*a*Sqrt[-n^(-2)]*n)*x)","A",3,2,28,0.07143,1,"{4493, 4489}"
46,1,178,0,0.1138349,"\int \frac{\sin ^3\left(a+\frac{2}{3} \sqrt{-\frac{1}{n^2}} \log \left(c x^n\right)\right)}{x^3} \, dx","Int[Sin[a + (2*Sqrt[-n^(-2)]*Log[c*x^n])/3]^3/x^3,x]","-\frac{\sqrt{-\frac{1}{n^2}} n e^{3 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{-2/n}}{32 x^2}+\frac{9 \sqrt{-\frac{1}{n^2}} n e^{a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.-\frac{2}{3}\right/n}}{64 x^2}-\frac{9 \sqrt{-\frac{1}{n^2}} n e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.\frac{2}{3}\right/n}}{32 x^2}-\frac{\sqrt{-\frac{1}{n^2}} n e^{-3 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{2/n}}{8 x^2}","-\frac{\sqrt{-\frac{1}{n^2}} n e^{3 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{-2/n}}{32 x^2}+\frac{9 \sqrt{-\frac{1}{n^2}} n e^{a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.-\frac{2}{3}\right/n}}{64 x^2}-\frac{9 \sqrt{-\frac{1}{n^2}} n e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.\frac{2}{3}\right/n}}{32 x^2}-\frac{\sqrt{-\frac{1}{n^2}} n e^{-3 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{2/n}}{8 x^2}",1,"-(E^(3*a*Sqrt[-n^(-2)]*n)*Sqrt[-n^(-2)]*n)/(32*x^2*(c*x^n)^(2/n)) + (9*E^(a*Sqrt[-n^(-2)]*n)*Sqrt[-n^(-2)]*n)/(64*x^2*(c*x^n)^(2/(3*n))) - (9*Sqrt[-n^(-2)]*n*(c*x^n)^(2/(3*n)))/(32*E^(a*Sqrt[-n^(-2)]*n)*x^2) - (Sqrt[-n^(-2)]*n*(c*x^n)^(2/n)*Log[x])/(8*E^(3*a*Sqrt[-n^(-2)]*n)*x^2)","A",3,2,28,0.07143,1,"{4493, 4489}"
47,1,112,0,0.1942043,"\int x^m \sin \left(a+\frac{1}{2} \sqrt{-(1+m)^2} \log \left(c x^2\right)\right) \, dx","Int[x^m*Sin[a + (Sqrt[-(1 + m)^2]*Log[c*x^2])/2],x]","\frac{(m+1) e^{\frac{a \sqrt{-(m+1)^2}}{m+1}} x^{m+1} \log (x) \left(c x^2\right)^{\frac{1}{2} (-m-1)}}{2 \sqrt{-(m+1)^2}}-\frac{e^{\frac{a (m+1)}{\sqrt{-(m+1)^2}}} x^{m+1} \left(c x^2\right)^{\frac{m+1}{2}}}{4 \sqrt{-(m+1)^2}}","\frac{(m+1) e^{\frac{a \sqrt{-(m+1)^2}}{m+1}} x^{m+1} \log (x) \left(c x^2\right)^{\frac{1}{2} (-m-1)}}{2 \sqrt{-(m+1)^2}}-\frac{e^{\frac{a (m+1)}{\sqrt{-(m+1)^2}}} x^{m+1} \left(c x^2\right)^{\frac{m+1}{2}}}{4 \sqrt{-(m+1)^2}}",1,"-(E^((a*(1 + m))/Sqrt[-(1 + m)^2])*x^(1 + m)*(c*x^2)^((1 + m)/2))/(4*Sqrt[-(1 + m)^2]) + (E^((a*Sqrt[-(1 + m)^2])/(1 + m))*(1 + m)*x^(1 + m)*(c*x^2)^((-1 - m)/2)*Log[x])/(2*Sqrt[-(1 + m)^2])","A",3,2,28,0.07143,1,"{4493, 4489}"
48,1,52,0,0.0354132,"\int \sin \left(a+\frac{1}{2} i \log \left(c x^2\right)\right) \, dx","Int[Sin[a + (I/2)*Log[c*x^2]],x]","\frac{i e^{-i a} c x^3}{4 \sqrt{c x^2}}-\frac{i e^{i a} x \log (x)}{2 \sqrt{c x^2}}","\frac{i e^{-i a} c x^3}{4 \sqrt{c x^2}}-\frac{i e^{i a} x \log (x)}{2 \sqrt{c x^2}}",1,"((I/4)*c*x^3)/(E^(I*a)*Sqrt[c*x^2]) - ((I/2)*E^(I*a)*x*Log[x])/Sqrt[c*x^2]","A",3,2,15,0.1333,1,"{4483, 4489}"
49,1,106,0,0.1446704,"\int x^m \sin ^2\left(a+\frac{1}{4} \sqrt{-(1+m)^2} \log \left(c x^2\right)\right) \, dx","Int[x^m*Sin[a + (Sqrt[-(1 + m)^2]*Log[c*x^2])/4]^2,x]","-\frac{e^{\frac{2 a (m+1)}{\sqrt{-(m+1)^2}}} x^{m+1} \left(c x^2\right)^{\frac{m+1}{2}}}{8 (m+1)}-\frac{1}{4} e^{-\frac{2 a (m+1)}{\sqrt{-(m+1)^2}}} x^{m+1} \log (x) \left(c x^2\right)^{\frac{1}{2} (-m-1)}+\frac{x^{m+1}}{2 (m+1)}","-\frac{e^{\frac{2 a (m+1)}{\sqrt{-(m+1)^2}}} x^{m+1} \left(c x^2\right)^{\frac{m+1}{2}}}{8 (m+1)}-\frac{1}{4} e^{-\frac{2 a (m+1)}{\sqrt{-(m+1)^2}}} x^{m+1} \log (x) \left(c x^2\right)^{\frac{1}{2} (-m-1)}+\frac{x^{m+1}}{2 (m+1)}",1,"x^(1 + m)/(2*(1 + m)) - (E^((2*a*(1 + m))/Sqrt[-(1 + m)^2])*x^(1 + m)*(c*x^2)^((1 + m)/2))/(8*(1 + m)) - (x^(1 + m)*(c*x^2)^((-1 - m)/2)*Log[x])/(4*E^((2*a*(1 + m))/Sqrt[-(1 + m)^2]))","A",3,2,30,0.06667,1,"{4493, 4489}"
50,1,53,0,0.0452294,"\int \sin ^2\left(a+\frac{1}{4} i \log \left(c x^2\right)\right) \, dx","Int[Sin[a + (I/4)*Log[c*x^2]]^2,x]","-\frac{e^{-2 i a} c x^3}{8 \sqrt{c x^2}}-\frac{e^{2 i a} x \log (x)}{4 \sqrt{c x^2}}+\frac{x}{2}","-\frac{e^{-2 i a} c x^3}{8 \sqrt{c x^2}}-\frac{e^{2 i a} x \log (x)}{4 \sqrt{c x^2}}+\frac{x}{2}",1,"x/2 - (c*x^3)/(8*E^((2*I)*a)*Sqrt[c*x^2]) - (E^((2*I)*a)*x*Log[x])/(4*Sqrt[c*x^2])","A",3,2,17,0.1176,1,"{4483, 4489}"
51,1,218,0,0.3045949,"\int x^m \sin ^3\left(a+\frac{1}{6} \sqrt{-(1+m)^2} \log \left(c x^2\right)\right) \, dx","Int[x^m*Sin[a + (Sqrt[-(1 + m)^2]*Log[c*x^2])/6]^3,x]","\frac{9 e^{\frac{a \sqrt{-(m+1)^2}}{m+1}} x^{m+1} \left(c x^2\right)^{\frac{1}{6} (-m-1)}}{16 \sqrt{-(m+1)^2}}-\frac{9 e^{\frac{a (m+1)}{\sqrt{-(m+1)^2}}} x^{m+1} \left(c x^2\right)^{\frac{m+1}{6}}}{32 \sqrt{-(m+1)^2}}+\frac{e^{\frac{3 a (m+1)}{\sqrt{-(m+1)^2}}} x^{m+1} \left(c x^2\right)^{\frac{m+1}{2}}}{16 \sqrt{-(m+1)^2}}-\frac{(m+1) e^{-\frac{3 a (m+1)}{\sqrt{-(m+1)^2}}} x^{m+1} \log (x) \left(c x^2\right)^{\frac{1}{2} (-m-1)}}{8 \sqrt{-(m+1)^2}}","\frac{9 e^{\frac{a \sqrt{-(m+1)^2}}{m+1}} x^{m+1} \left(c x^2\right)^{\frac{1}{6} (-m-1)}}{16 \sqrt{-(m+1)^2}}-\frac{9 e^{\frac{a (m+1)}{\sqrt{-(m+1)^2}}} x^{m+1} \left(c x^2\right)^{\frac{m+1}{6}}}{32 \sqrt{-(m+1)^2}}+\frac{e^{\frac{3 a (m+1)}{\sqrt{-(m+1)^2}}} x^{m+1} \left(c x^2\right)^{\frac{m+1}{2}}}{16 \sqrt{-(m+1)^2}}-\frac{(m+1) e^{-\frac{3 a (m+1)}{\sqrt{-(m+1)^2}}} x^{m+1} \log (x) \left(c x^2\right)^{\frac{1}{2} (-m-1)}}{8 \sqrt{-(m+1)^2}}",1,"(9*E^((a*Sqrt[-(1 + m)^2])/(1 + m))*x^(1 + m)*(c*x^2)^((-1 - m)/6))/(16*Sqrt[-(1 + m)^2]) - (9*E^((a*(1 + m))/Sqrt[-(1 + m)^2])*x^(1 + m)*(c*x^2)^((1 + m)/6))/(32*Sqrt[-(1 + m)^2]) + (E^((3*a*(1 + m))/Sqrt[-(1 + m)^2])*x^(1 + m)*(c*x^2)^((1 + m)/2))/(16*Sqrt[-(1 + m)^2]) - ((1 + m)*x^(1 + m)*(c*x^2)^((-1 - m)/2)*Log[x])/(8*E^((3*a*(1 + m))/Sqrt[-(1 + m)^2])*Sqrt[-(1 + m)^2])","A",3,2,30,0.06667,1,"{4493, 4489}"
52,1,98,0,0.0609948,"\int \sin ^3\left(a+\frac{1}{6} i \log \left(c x^2\right)\right) \, dx","Int[Sin[a + (I/6)*Log[c*x^2]]^3,x]","-\frac{i e^{-3 i a} c x^3}{16 \sqrt{c x^2}}+\frac{9}{32} i e^{-i a} x \sqrt[6]{c x^2}-\frac{9 i e^{i a} x}{16 \sqrt[6]{c x^2}}+\frac{i e^{3 i a} x \log (x)}{8 \sqrt{c x^2}}","-\frac{i e^{-3 i a} c x^3}{16 \sqrt{c x^2}}+\frac{9}{32} i e^{-i a} x \sqrt[6]{c x^2}-\frac{9 i e^{i a} x}{16 \sqrt[6]{c x^2}}+\frac{i e^{3 i a} x \log (x)}{8 \sqrt{c x^2}}",1,"((-I/16)*c*x^3)/(E^((3*I)*a)*Sqrt[c*x^2]) - (((9*I)/16)*E^(I*a)*x)/(c*x^2)^(1/6) + (((9*I)/32)*x*(c*x^2)^(1/6))/E^(I*a) + ((I/8)*E^((3*I)*a)*x*Log[x])/Sqrt[c*x^2]","A",3,2,17,0.1176,1,"{4483, 4489}"
53,1,111,0,0.0860572,"\int x \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)} \, dx","Int[x*Sqrt[Sin[a + b*Log[c*x^n]]],x]","\frac{2 x^2 \, _2F_1\left(-\frac{1}{2},\frac{1}{4} \left(-1-\frac{4 i}{b n}\right);\frac{1}{4} \left(3-\frac{4 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)}}{(4-i b n) \sqrt{1-e^{2 i a} \left(c x^n\right)^{2 i b}}}","\frac{2 x^2 \, _2F_1\left(-\frac{1}{2},\frac{1}{4} \left(-1-\frac{4 i}{b n}\right);\frac{1}{4} \left(3-\frac{4 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)}}{(4-i b n) \sqrt{1-e^{2 i a} \left(c x^n\right)^{2 i b}}}",1,"(2*x^2*Hypergeometric2F1[-1/2, (-1 - (4*I)/(b*n))/4, (3 - (4*I)/(b*n))/4, E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Sqrt[Sin[a + b*Log[c*x^n]]])/((4 - I*b*n)*Sqrt[1 - E^((2*I)*a)*(c*x^n)^((2*I)*b)])","A",3,3,17,0.1765,1,"{4493, 4491, 364}"
54,1,110,0,0.0749734,"\int \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)} \, dx","Int[Sqrt[Sin[a + b*Log[c*x^n]]],x]","\frac{2 x \, _2F_1\left(-\frac{1}{2},-\frac{b n+2 i}{4 b n};\frac{1}{4} \left(3-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)}}{(2-i b n) \sqrt{1-e^{2 i a} \left(c x^n\right)^{2 i b}}}","\frac{2 x \, _2F_1\left(-\frac{1}{2},-\frac{b n+2 i}{4 b n};\frac{1}{4} \left(3-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)}}{(2-i b n) \sqrt{1-e^{2 i a} \left(c x^n\right)^{2 i b}}}",1,"(2*x*Hypergeometric2F1[-1/2, -(2*I + b*n)/(4*b*n), (3 - (2*I)/(b*n))/4, E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Sqrt[Sin[a + b*Log[c*x^n]]])/((2 - I*b*n)*Sqrt[1 - E^((2*I)*a)*(c*x^n)^((2*I)*b)])","A",3,3,15,0.2000,1,"{4483, 4491, 364}"
55,1,29,0,0.0273205,"\int \frac{\sqrt{\sin \left(a+b \log \left(c x^n\right)\right)}}{x} \, dx","Int[Sqrt[Sin[a + b*Log[c*x^n]]]/x,x]","\frac{2 E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{b n}","\frac{2 E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{b n}",1,"(2*EllipticE[(a - Pi/2 + b*Log[c*x^n])/2, 2])/(b*n)","A",2,1,19,0.05263,1,"{2639}"
56,1,111,0,0.0880578,"\int \frac{\sqrt{\sin \left(a+b \log \left(c x^n\right)\right)}}{x^2} \, dx","Int[Sqrt[Sin[a + b*Log[c*x^n]]]/x^2,x]","-\frac{2 \, _2F_1\left(-\frac{1}{2},\frac{1}{4} \left(\frac{2 i}{b n}-1\right);\frac{1}{4} \left(3+\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)}}{x (2+i b n) \sqrt{1-e^{2 i a} \left(c x^n\right)^{2 i b}}}","-\frac{2 \, _2F_1\left(-\frac{1}{2},\frac{1}{4} \left(\frac{2 i}{b n}-1\right);\frac{1}{4} \left(3+\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)}}{x (2+i b n) \sqrt{1-e^{2 i a} \left(c x^n\right)^{2 i b}}}",1,"(-2*Hypergeometric2F1[-1/2, (-1 + (2*I)/(b*n))/4, (3 + (2*I)/(b*n))/4, E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Sqrt[Sin[a + b*Log[c*x^n]]])/((2 + I*b*n)*x*Sqrt[1 - E^((2*I)*a)*(c*x^n)^((2*I)*b)])","A",3,3,19,0.1579,1,"{4493, 4491, 364}"
57,1,111,0,0.0897216,"\int \frac{\sqrt{\sin \left(a+b \log \left(c x^n\right)\right)}}{x^3} \, dx","Int[Sqrt[Sin[a + b*Log[c*x^n]]]/x^3,x]","-\frac{2 \, _2F_1\left(-\frac{1}{2},\frac{1}{4} \left(\frac{4 i}{b n}-1\right);\frac{1}{4} \left(3+\frac{4 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)}}{x^2 (4+i b n) \sqrt{1-e^{2 i a} \left(c x^n\right)^{2 i b}}}","-\frac{2 \, _2F_1\left(-\frac{1}{2},\frac{1}{4} \left(\frac{4 i}{b n}-1\right);\frac{1}{4} \left(3+\frac{4 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)}}{x^2 (4+i b n) \sqrt{1-e^{2 i a} \left(c x^n\right)^{2 i b}}}",1,"(-2*Hypergeometric2F1[-1/2, (-1 + (4*I)/(b*n))/4, (3 + (4*I)/(b*n))/4, E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Sqrt[Sin[a + b*Log[c*x^n]]])/((4 + I*b*n)*x^2*Sqrt[1 - E^((2*I)*a)*(c*x^n)^((2*I)*b)])","A",3,3,19,0.1579,1,"{4493, 4491, 364}"
58,1,111,0,0.0780123,"\int x \sin ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Sin[a + b*Log[c*x^n]]^(3/2),x]","\frac{2 x^2 \, _2F_1\left(-\frac{3}{2},\frac{1}{4} \left(-3-\frac{4 i}{b n}\right);\frac{1}{4} \left(1-\frac{4 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sin ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{(4-3 i b n) \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2}}","\frac{2 x^2 \, _2F_1\left(-\frac{3}{2},\frac{1}{4} \left(-3-\frac{4 i}{b n}\right);\frac{1}{4} \left(1-\frac{4 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sin ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{(4-3 i b n) \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2}}",1,"(2*x^2*Hypergeometric2F1[-3/2, (-3 - (4*I)/(b*n))/4, (1 - (4*I)/(b*n))/4, E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Sin[a + b*Log[c*x^n]]^(3/2))/((4 - (3*I)*b*n)*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^(3/2))","A",3,3,17,0.1765,1,"{4493, 4491, 364}"
59,1,109,0,0.0727374,"\int \sin ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sin[a + b*Log[c*x^n]]^(3/2),x]","\frac{2 x \, _2F_1\left(-\frac{3}{2},\frac{1}{4} \left(-3-\frac{2 i}{b n}\right);\frac{1}{4} \left(1-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sin ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{(2-3 i b n) \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2}}","\frac{2 x \, _2F_1\left(-\frac{3}{2},\frac{1}{4} \left(-3-\frac{2 i}{b n}\right);\frac{1}{4} \left(1-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sin ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{(2-3 i b n) \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2}}",1,"(2*x*Hypergeometric2F1[-3/2, (-3 - (2*I)/(b*n))/4, (1 - (2*I)/(b*n))/4, E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Sin[a + b*Log[c*x^n]]^(3/2))/((2 - (3*I)*b*n)*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^(3/2))","A",3,3,15,0.2000,1,"{4483, 4491, 364}"
60,1,68,0,0.0418833,"\int \frac{\sin ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Sin[a + b*Log[c*x^n]]^(3/2)/x,x]","\frac{2 F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{3 b n}-\frac{2 \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)} \cos \left(a+b \log \left(c x^n\right)\right)}{3 b n}","\frac{2 F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{3 b n}-\frac{2 \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)} \cos \left(a+b \log \left(c x^n\right)\right)}{3 b n}",1,"(2*EllipticF[(a - Pi/2 + b*Log[c*x^n])/2, 2])/(3*b*n) - (2*Cos[a + b*Log[c*x^n]]*Sqrt[Sin[a + b*Log[c*x^n]]])/(3*b*n)","A",3,2,19,0.1053,1,"{2635, 2641}"
61,1,111,0,0.0875124,"\int \frac{\sin ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[Sin[a + b*Log[c*x^n]]^(3/2)/x^2,x]","-\frac{2 \, _2F_1\left(-\frac{3}{2},\frac{1}{4} \left(\frac{2 i}{b n}-3\right);\frac{1}{4} \left(1+\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sin ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x (2+3 i b n) \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2}}","-\frac{2 \, _2F_1\left(-\frac{3}{2},\frac{1}{4} \left(\frac{2 i}{b n}-3\right);\frac{1}{4} \left(1+\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sin ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x (2+3 i b n) \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2}}",1,"(-2*Hypergeometric2F1[-3/2, (-3 + (2*I)/(b*n))/4, (1 + (2*I)/(b*n))/4, E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Sin[a + b*Log[c*x^n]]^(3/2))/((2 + (3*I)*b*n)*x*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^(3/2))","A",3,3,19,0.1579,1,"{4493, 4491, 364}"
62,1,111,0,0.0869713,"\int \frac{\sin ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[Sin[a + b*Log[c*x^n]]^(3/2)/x^3,x]","-\frac{2 \, _2F_1\left(-\frac{3}{2},\frac{1}{4} \left(\frac{4 i}{b n}-3\right);\frac{1}{4} \left(1+\frac{4 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sin ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x^2 (4+3 i b n) \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2}}","-\frac{2 \, _2F_1\left(-\frac{3}{2},\frac{1}{4} \left(\frac{4 i}{b n}-3\right);\frac{1}{4} \left(1+\frac{4 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sin ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x^2 (4+3 i b n) \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2}}",1,"(-2*Hypergeometric2F1[-3/2, (-3 + (4*I)/(b*n))/4, (1 + (4*I)/(b*n))/4, E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Sin[a + b*Log[c*x^n]]^(3/2))/((4 + (3*I)*b*n)*x^2*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^(3/2))","A",3,3,19,0.1579,1,"{4493, 4491, 364}"
63,1,109,0,0.0695574,"\int \frac{1}{\sqrt{\sin \left(a+b \log \left(c x^n\right)\right)}} \, dx","Int[1/Sqrt[Sin[a + b*Log[c*x^n]]],x]","\frac{2 x \sqrt{1-e^{2 i a} \left(c x^n\right)^{2 i b}} \, _2F_1\left(\frac{1}{2},\frac{1}{4} \left(1-\frac{2 i}{b n}\right);\frac{1}{4} \left(5-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2+i b n) \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)}}","\frac{2 x \sqrt{1-e^{2 i a} \left(c x^n\right)^{2 i b}} \, _2F_1\left(\frac{1}{2},\frac{1}{4} \left(1-\frac{2 i}{b n}\right);\frac{1}{4} \left(5-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2+i b n) \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)}}",1,"(2*x*Sqrt[1 - E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Hypergeometric2F1[1/2, (1 - (2*I)/(b*n))/4, (5 - (2*I)/(b*n))/4, E^((2*I)*a)*(c*x^n)^((2*I)*b)])/((2 + I*b*n)*Sqrt[Sin[a + b*Log[c*x^n]]])","A",3,3,15,0.2000,1,"{4483, 4491, 364}"
64,1,29,0,0.0265995,"\int \frac{1}{x \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)}} \, dx","Int[1/(x*Sqrt[Sin[a + b*Log[c*x^n]]]),x]","\frac{2 F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{b n}","\frac{2 F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{b n}",1,"(2*EllipticF[(a - Pi/2 + b*Log[c*x^n])/2, 2])/(b*n)","A",2,1,19,0.05263,1,"{2641}"
65,1,109,0,0.0703636,"\int \frac{1}{\sin ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[Sin[a + b*Log[c*x^n]]^(-3/2),x]","\frac{2 x \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{1}{4} \left(3-\frac{2 i}{b n}\right);\frac{1}{4} \left(7-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2+3 i b n) \sin ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}","\frac{2 x \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{1}{4} \left(3-\frac{2 i}{b n}\right);\frac{1}{4} \left(7-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2+3 i b n) \sin ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}",1,"(2*x*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^(3/2)*Hypergeometric2F1[3/2, (3 - (2*I)/(b*n))/4, (7 - (2*I)/(b*n))/4, E^((2*I)*a)*(c*x^n)^((2*I)*b)])/((2 + (3*I)*b*n)*Sin[a + b*Log[c*x^n]]^(3/2))","A",3,3,15,0.2000,1,"{4483, 4491, 364}"
66,1,64,0,0.0423166,"\int \frac{1}{x \sin ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[1/(x*Sin[a + b*Log[c*x^n]]^(3/2)),x]","-\frac{2 E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{b n}-\frac{2 \cos \left(a+b \log \left(c x^n\right)\right)}{b n \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)}}","-\frac{2 E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{b n}-\frac{2 \cos \left(a+b \log \left(c x^n\right)\right)}{b n \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)}}",1,"(-2*EllipticE[(a - Pi/2 + b*Log[c*x^n])/2, 2])/(b*n) - (2*Cos[a + b*Log[c*x^n]])/(b*n*Sqrt[Sin[a + b*Log[c*x^n]]])","A",3,2,19,0.1053,1,"{2636, 2639}"
67,1,109,0,0.0738603,"\int \frac{1}{\sin ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[Sin[a + b*Log[c*x^n]]^(-5/2),x]","\frac{2 x \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2} \, _2F_1\left(\frac{5}{2},\frac{1}{4} \left(5-\frac{2 i}{b n}\right);\frac{1}{4} \left(9-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2+5 i b n) \sin ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}","\frac{2 x \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2} \, _2F_1\left(\frac{5}{2},\frac{1}{4} \left(5-\frac{2 i}{b n}\right);\frac{1}{4} \left(9-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2+5 i b n) \sin ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}",1,"(2*x*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^(5/2)*Hypergeometric2F1[5/2, (5 - (2*I)/(b*n))/4, (9 - (2*I)/(b*n))/4, E^((2*I)*a)*(c*x^n)^((2*I)*b)])/((2 + (5*I)*b*n)*Sin[a + b*Log[c*x^n]]^(5/2))","A",3,3,15,0.2000,1,"{4483, 4491, 364}"
68,1,68,0,0.0421785,"\int \frac{1}{x \sin ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[1/(x*Sin[a + b*Log[c*x^n]]^(5/2)),x]","\frac{2 F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{3 b n}-\frac{2 \cos \left(a+b \log \left(c x^n\right)\right)}{3 b n \sin ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}","\frac{2 F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{3 b n}-\frac{2 \cos \left(a+b \log \left(c x^n\right)\right)}{3 b n \sin ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}",1,"(2*EllipticF[(a - Pi/2 + b*Log[c*x^n])/2, 2])/(3*b*n) - (2*Cos[a + b*Log[c*x^n]])/(3*b*n*Sin[a + b*Log[c*x^n]]^(3/2))","A",3,2,19,0.1053,1,"{2636, 2641}"
69,1,49,0,0.0389924,"\int \frac{1}{\sin ^{\frac{3}{2}}(a-2 i \log (c x))} \, dx","Int[Sin[a - (2*I)*Log[c*x]]^(-3/2),x]","\frac{e^{-2 i a} \left(1-e^{2 i a} c^4 x^4\right)}{2 c^4 x^3 \sin ^{\frac{3}{2}}(a-2 i \log (c x))}","\frac{e^{-2 i a} \left(1-e^{2 i a} c^4 x^4\right)}{2 c^4 x^3 \sin ^{\frac{3}{2}}(a-2 i \log (c x))}",1,"(1 - c^4*E^((2*I)*a)*x^4)/(2*c^4*E^((2*I)*a)*x^3*Sin[a - (2*I)*Log[c*x]]^(3/2))","A",3,3,15,0.2000,1,"{4483, 4481, 261}"
70,1,337,0,0.1695101,"\int (e x)^m \sin ^4\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Sin[d*(a + b*Log[c*x^n])]^4,x]","\frac{(m+1) (e x)^{m+1} \sin ^4\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(16 b^2 d^2 n^2+(m+1)^2\right)}+\frac{12 b^2 d^2 (m+1) n^2 (e x)^{m+1} \sin ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(4 b^2 d^2 n^2+(m+1)^2\right) \left(16 b^2 d^2 n^2+(m+1)^2\right)}-\frac{4 b d n (e x)^{m+1} \sin ^3\left(d \left(a+b \log \left(c x^n\right)\right)\right) \cos \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(16 b^2 d^2 n^2+(m+1)^2\right)}-\frac{24 b^3 d^3 n^3 (e x)^{m+1} \sin \left(d \left(a+b \log \left(c x^n\right)\right)\right) \cos \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(4 b^2 d^2 n^2+(m+1)^2\right) \left(16 b^2 d^2 n^2+(m+1)^2\right)}+\frac{24 b^4 d^4 n^4 (e x)^{m+1}}{e (m+1) \left(4 b^2 d^2 n^2+(m+1)^2\right) \left(16 b^2 d^2 n^2+(m+1)^2\right)}","\frac{(m+1) (e x)^{m+1} \sin ^4\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(16 b^2 d^2 n^2+(m+1)^2\right)}+\frac{12 b^2 d^2 (m+1) n^2 (e x)^{m+1} \sin ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(4 b^2 d^2 n^2+(m+1)^2\right) \left(16 b^2 d^2 n^2+(m+1)^2\right)}-\frac{4 b d n (e x)^{m+1} \sin ^3\left(d \left(a+b \log \left(c x^n\right)\right)\right) \cos \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(16 b^2 d^2 n^2+(m+1)^2\right)}-\frac{24 b^3 d^3 n^3 (e x)^{m+1} \sin \left(d \left(a+b \log \left(c x^n\right)\right)\right) \cos \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(4 b^2 d^2 n^2+(m+1)^2\right) \left(16 b^2 d^2 n^2+(m+1)^2\right)}+\frac{24 b^4 d^4 n^4 (e x)^{m+1}}{e (m+1) \left(4 b^2 d^2 n^2+(m+1)^2\right) \left(16 b^2 d^2 n^2+(m+1)^2\right)}",1,"(24*b^4*d^4*n^4*(e*x)^(1 + m))/(e*(1 + m)*((1 + m)^2 + 4*b^2*d^2*n^2)*((1 + m)^2 + 16*b^2*d^2*n^2)) - (24*b^3*d^3*n^3*(e*x)^(1 + m)*Cos[d*(a + b*Log[c*x^n])]*Sin[d*(a + b*Log[c*x^n])])/(e*((1 + m)^2 + 4*b^2*d^2*n^2)*((1 + m)^2 + 16*b^2*d^2*n^2)) + (12*b^2*d^2*(1 + m)*n^2*(e*x)^(1 + m)*Sin[d*(a + b*Log[c*x^n])]^2)/(e*((1 + m)^2 + 4*b^2*d^2*n^2)*((1 + m)^2 + 16*b^2*d^2*n^2)) - (4*b*d*n*(e*x)^(1 + m)*Cos[d*(a + b*Log[c*x^n])]*Sin[d*(a + b*Log[c*x^n])]^3)/(e*((1 + m)^2 + 16*b^2*d^2*n^2)) + ((1 + m)*(e*x)^(1 + m)*Sin[d*(a + b*Log[c*x^n])]^4)/(e*((1 + m)^2 + 16*b^2*d^2*n^2))","A",3,2,21,0.09524,1,"{4487, 32}"
71,1,256,0,0.1179071,"\int (e x)^m \sin ^3\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Sin[d*(a + b*Log[c*x^n])]^3,x]","\frac{(m+1) (e x)^{m+1} \sin ^3\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(9 b^2 d^2 n^2+(m+1)^2\right)}+\frac{6 b^2 d^2 (m+1) n^2 (e x)^{m+1} \sin \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(b^2 d^2 n^2+(m+1)^2\right) \left(9 b^2 d^2 n^2+(m+1)^2\right)}-\frac{6 b^3 d^3 n^3 (e x)^{m+1} \cos \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(b^2 d^2 n^2+(m+1)^2\right) \left(9 b^2 d^2 n^2+(m+1)^2\right)}-\frac{3 b d n (e x)^{m+1} \sin ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \cos \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(9 b^2 d^2 n^2+(m+1)^2\right)}","\frac{(m+1) (e x)^{m+1} \sin ^3\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(9 b^2 d^2 n^2+(m+1)^2\right)}+\frac{6 b^2 d^2 (m+1) n^2 (e x)^{m+1} \sin \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(b^2 d^2 n^2+(m+1)^2\right) \left(9 b^2 d^2 n^2+(m+1)^2\right)}-\frac{6 b^3 d^3 n^3 (e x)^{m+1} \cos \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(b^2 d^2 n^2+(m+1)^2\right) \left(9 b^2 d^2 n^2+(m+1)^2\right)}-\frac{3 b d n (e x)^{m+1} \sin ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \cos \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(9 b^2 d^2 n^2+(m+1)^2\right)}",1,"(-6*b^3*d^3*n^3*(e*x)^(1 + m)*Cos[d*(a + b*Log[c*x^n])])/(e*((1 + m)^2 + b^2*d^2*n^2)*((1 + m)^2 + 9*b^2*d^2*n^2)) + (6*b^2*d^2*(1 + m)*n^2*(e*x)^(1 + m)*Sin[d*(a + b*Log[c*x^n])])/(e*((1 + m)^2 + b^2*d^2*n^2)*((1 + m)^2 + 9*b^2*d^2*n^2)) - (3*b*d*n*(e*x)^(1 + m)*Cos[d*(a + b*Log[c*x^n])]*Sin[d*(a + b*Log[c*x^n])]^2)/(e*((1 + m)^2 + 9*b^2*d^2*n^2)) + ((1 + m)*(e*x)^(1 + m)*Sin[d*(a + b*Log[c*x^n])]^3)/(e*((1 + m)^2 + 9*b^2*d^2*n^2))","A",2,2,21,0.09524,1,"{4487, 4485}"
72,1,154,0,0.055039,"\int (e x)^m \sin ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Sin[d*(a + b*Log[c*x^n])]^2,x]","\frac{(m+1) (e x)^{m+1} \sin ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(4 b^2 d^2 n^2+(m+1)^2\right)}-\frac{2 b d n (e x)^{m+1} \sin \left(d \left(a+b \log \left(c x^n\right)\right)\right) \cos \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(4 b^2 d^2 n^2+(m+1)^2\right)}+\frac{2 b^2 d^2 n^2 (e x)^{m+1}}{e (m+1) \left(4 b^2 d^2 n^2+(m+1)^2\right)}","\frac{(m+1) (e x)^{m+1} \sin ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(4 b^2 d^2 n^2+(m+1)^2\right)}-\frac{2 b d n (e x)^{m+1} \sin \left(d \left(a+b \log \left(c x^n\right)\right)\right) \cos \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(4 b^2 d^2 n^2+(m+1)^2\right)}+\frac{2 b^2 d^2 n^2 (e x)^{m+1}}{e (m+1) \left(4 b^2 d^2 n^2+(m+1)^2\right)}",1,"(2*b^2*d^2*n^2*(e*x)^(1 + m))/(e*(1 + m)*((1 + m)^2 + 4*b^2*d^2*n^2)) - (2*b*d*n*(e*x)^(1 + m)*Cos[d*(a + b*Log[c*x^n])]*Sin[d*(a + b*Log[c*x^n])])/(e*((1 + m)^2 + 4*b^2*d^2*n^2)) + ((1 + m)*(e*x)^(1 + m)*Sin[d*(a + b*Log[c*x^n])]^2)/(e*((1 + m)^2 + 4*b^2*d^2*n^2))","A",2,2,21,0.09524,1,"{4487, 32}"
73,1,92,0,0.0245137,"\int (e x)^m \sin \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Sin[d*(a + b*Log[c*x^n])],x]","\frac{(m+1) (e x)^{m+1} \sin \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(b^2 d^2 n^2+(m+1)^2\right)}-\frac{b d n (e x)^{m+1} \cos \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(b^2 d^2 n^2+(m+1)^2\right)}","\frac{(m+1) (e x)^{m+1} \sin \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(b^2 d^2 n^2+(m+1)^2\right)}-\frac{b d n (e x)^{m+1} \cos \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e \left(b^2 d^2 n^2+(m+1)^2\right)}",1,"-((b*d*n*(e*x)^(1 + m)*Cos[d*(a + b*Log[c*x^n])])/(e*((1 + m)^2 + b^2*d^2*n^2))) + ((1 + m)*(e*x)^(1 + m)*Sin[d*(a + b*Log[c*x^n])])/(e*((1 + m)^2 + b^2*d^2*n^2))","A",1,1,19,0.05263,1,"{4485}"
74,1,145,0,0.1255275,"\int (e x)^m \sin ^{\frac{3}{2}}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Sin[d*(a + b*Log[c*x^n])]^(3/2),x]","\frac{2 (e x)^{m+1} \, _2F_1\left(-\frac{3}{2},\frac{1}{4} \left(-\frac{2 i (m+1)}{b d n}-3\right);-\frac{2 i m-b d n+2 i}{4 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right) \sin ^{\frac{3}{2}}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e (-3 i b d n+2 m+2) \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^{3/2}}","\frac{2 (e x)^{m+1} \, _2F_1\left(-\frac{3}{2},-\frac{2 i m+3 b d n+2 i}{4 b d n};-\frac{2 i m-b d n+2 i}{4 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right) \sin ^{\frac{3}{2}}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e (-3 i b d n+2 m+2) \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^{3/2}}",1,"(2*(e*x)^(1 + m)*Hypergeometric2F1[-3/2, (-3 - ((2*I)*(1 + m))/(b*d*n))/4, -(2*I + (2*I)*m - b*d*n)/(4*b*d*n), E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d)]*Sin[d*(a + b*Log[c*x^n])]^(3/2))/(e*(2 + 2*m - (3*I)*b*d*n)*(1 - E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d))^(3/2))","A",3,3,23,0.1304,1,"{4493, 4491, 364}"
75,1,145,0,0.1118696,"\int (e x)^m \sqrt{\sin \left(d \left(a+b \log \left(c x^n\right)\right)\right)} \, dx","Int[(e*x)^m*Sqrt[Sin[d*(a + b*Log[c*x^n])]],x]","\frac{2 (e x)^{m+1} \, _2F_1\left(-\frac{1}{2},\frac{1}{4} \left(-\frac{2 i (m+1)}{b d n}-1\right);-\frac{2 i m-3 b d n+2 i}{4 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right) \sqrt{\sin \left(d \left(a+b \log \left(c x^n\right)\right)\right)}}{e (-i b d n+2 m+2) \sqrt{1-e^{2 i a d} \left(c x^n\right)^{2 i b d}}}","\frac{2 (e x)^{m+1} \, _2F_1\left(-\frac{1}{2},-\frac{2 i m+b d n+2 i}{4 b d n};-\frac{2 i m-3 b d n+2 i}{4 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right) \sqrt{\sin \left(d \left(a+b \log \left(c x^n\right)\right)\right)}}{e (-i b d n+2 m+2) \sqrt{1-e^{2 i a d} \left(c x^n\right)^{2 i b d}}}",1,"(2*(e*x)^(1 + m)*Hypergeometric2F1[-1/2, (-1 - ((2*I)*(1 + m))/(b*d*n))/4, -(2*I + (2*I)*m - 3*b*d*n)/(4*b*d*n), E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d)]*Sqrt[Sin[d*(a + b*Log[c*x^n])]])/(e*(2 + 2*m - I*b*d*n)*Sqrt[1 - E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d)])","A",3,3,23,0.1304,1,"{4493, 4491, 364}"
76,1,150,0,0.1099991,"\int \frac{(e x)^m}{\sqrt{\sin \left(d \left(a+b \log \left(c x^n\right)\right)\right)}} \, dx","Int[(e*x)^m/Sqrt[Sin[d*(a + b*Log[c*x^n])]],x]","\frac{2 (e x)^{m+1} \sqrt{1-e^{2 i a d} \left(c x^n\right)^{2 i b d}} \, _2F_1\left(\frac{1}{2},-\frac{2 i m-b d n+2 i}{4 b d n};-\frac{2 i m-5 b d n+2 i}{4 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{e (i b d n+2 m+2) \sqrt{\sin \left(d \left(a+b \log \left(c x^n\right)\right)\right)}}","\frac{2 (e x)^{m+1} \sqrt{1-e^{2 i a d} \left(c x^n\right)^{2 i b d}} \, _2F_1\left(\frac{1}{2},-\frac{2 i m-b d n+2 i}{4 b d n};-\frac{2 i m-5 b d n+2 i}{4 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{e (i b d n+2 m+2) \sqrt{\sin \left(d \left(a+b \log \left(c x^n\right)\right)\right)}}",1,"(2*(e*x)^(1 + m)*Sqrt[1 - E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d)]*Hypergeometric2F1[1/2, -(2*I + (2*I)*m - b*d*n)/(4*b*d*n), -(2*I + (2*I)*m - 5*b*d*n)/(4*b*d*n), E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d)])/(e*(2 + 2*m + I*b*d*n)*Sqrt[Sin[d*(a + b*Log[c*x^n])]])","A",3,3,23,0.1304,1,"{4493, 4491, 364}"
77,1,145,0,0.1130571,"\int \frac{(e x)^m}{\sin ^{\frac{3}{2}}\left(d \left(a+b \log \left(c x^n\right)\right)\right)} \, dx","Int[(e*x)^m/Sin[d*(a + b*Log[c*x^n])]^(3/2),x]","\frac{2 (e x)^{m+1} \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{1}{4} \left(3-\frac{2 i (m+1)}{b d n}\right);-\frac{2 i m-7 b d n+2 i}{4 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{e (3 i b d n+2 m+2) \sin ^{\frac{3}{2}}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}","\frac{2 (e x)^{m+1} \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^{3/2} \, _2F_1\left(\frac{3}{2},-\frac{2 i m-3 b d n+2 i}{4 b d n};-\frac{2 i m-7 b d n+2 i}{4 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{e (3 i b d n+2 m+2) \sin ^{\frac{3}{2}}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}",1,"(2*(e*x)^(1 + m)*(1 - E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d))^(3/2)*Hypergeometric2F1[3/2, (3 - ((2*I)*(1 + m))/(b*d*n))/4, -(2*I + (2*I)*m - 7*b*d*n)/(4*b*d*n), E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d)])/(e*(2 + 2*m + (3*I)*b*d*n)*Sin[d*(a + b*Log[c*x^n])]^(3/2))","A",3,3,23,0.1304,1,"{4493, 4491, 364}"
78,1,145,0,0.1137407,"\int \frac{(e x)^m}{\sin ^{\frac{5}{2}}\left(d \left(a+b \log \left(c x^n\right)\right)\right)} \, dx","Int[(e*x)^m/Sin[d*(a + b*Log[c*x^n])]^(5/2),x]","\frac{2 (e x)^{m+1} \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^{5/2} \, _2F_1\left(\frac{5}{2},\frac{1}{4} \left(5-\frac{2 i (m+1)}{b d n}\right);-\frac{2 i m-9 b d n+2 i}{4 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{e (5 i b d n+2 m+2) \sin ^{\frac{5}{2}}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}","\frac{2 (e x)^{m+1} \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^{5/2} \, _2F_1\left(\frac{5}{2},-\frac{2 i m-5 b d n+2 i}{4 b d n};-\frac{2 i m-9 b d n+2 i}{4 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{e (5 i b d n+2 m+2) \sin ^{\frac{5}{2}}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}",1,"(2*(e*x)^(1 + m)*(1 - E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d))^(5/2)*Hypergeometric2F1[5/2, (5 - ((2*I)*(1 + m))/(b*d*n))/4, -(2*I + (2*I)*m - 9*b*d*n)/(4*b*d*n), E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d)])/(e*(2 + 2*m + (5*I)*b*d*n)*Sin[d*(a + b*Log[c*x^n])]^(5/2))","A",3,3,23,0.1304,1,"{4493, 4491, 364}"
79,1,144,0,0.1225294,"\int (e x)^m \sin ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Sin[d*(a + b*Log[c*x^n])]^p,x]","\frac{(e x)^{m+1} \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^{-p} \, _2F_1\left(-p,-\frac{i m+b d n p+i}{2 b d n};\frac{1}{2} \left(-\frac{i (m+1)}{b d n}-p+2\right);e^{2 i a d} \left(c x^n\right)^{2 i b d}\right) \sin ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e (-i b d n p+m+1)}","\frac{(e x)^{m+1} \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^{-p} \, _2F_1\left(-p,-\frac{i m+b d n p+i}{2 b d n};\frac{1}{2} \left(-\frac{i (m+1)}{b d n}-p+2\right);e^{2 i a d} \left(c x^n\right)^{2 i b d}\right) \sin ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e (-i b d n p+m+1)}",1,"((e*x)^(1 + m)*Hypergeometric2F1[-p, -(I + I*m + b*d*n*p)/(2*b*d*n), (2 - (I*(1 + m))/(b*d*n) - p)/2, E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d)]*Sin[d*(a + b*Log[c*x^n])]^p)/(e*(1 + m - I*b*d*n*p)*(1 - E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d))^p)","A",3,3,21,0.1429,1,"{4493, 4491, 364}"
80,1,114,0,0.0950033,"\int x^2 \sin ^p\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*Sin[a + b*Log[c*x^n]]^p,x]","\frac{x^3 \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{-p} \, _2F_1\left(-p,-\frac{b n p+3 i}{2 b n};\frac{1}{2} \left(-p-\frac{3 i}{b n}+2\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sin ^p\left(a+b \log \left(c x^n\right)\right)}{3-i b n p}","\frac{x^3 \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{-p} \, _2F_1\left(-p,-\frac{b n p+3 i}{2 b n};\frac{1}{2} \left(-p-\frac{3 i}{b n}+2\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sin ^p\left(a+b \log \left(c x^n\right)\right)}{3-i b n p}",1,"(x^3*Hypergeometric2F1[-p, -(3*I + b*n*p)/(2*b*n), (2 - (3*I)/(b*n) - p)/2, E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Sin[a + b*Log[c*x^n]]^p)/((3 - I*b*n*p)*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^p)","A",3,3,17,0.1765,1,"{4493, 4491, 364}"
81,1,114,0,0.0831404,"\int x \sin ^p\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Sin[a + b*Log[c*x^n]]^p,x]","\frac{x^2 \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{-p} \, _2F_1\left(\frac{1}{2} \left(-p-\frac{2 i}{b n}\right),-p;\frac{1}{2} \left(-p-\frac{2 i}{b n}+2\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sin ^p\left(a+b \log \left(c x^n\right)\right)}{2-i b n p}","\frac{x^2 \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{-p} \, _2F_1\left(\frac{1}{2} \left(-p-\frac{2 i}{b n}\right),-p;\frac{1}{2} \left(-p-\frac{2 i}{b n}+2\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sin ^p\left(a+b \log \left(c x^n\right)\right)}{2-i b n p}",1,"(x^2*Hypergeometric2F1[((-2*I)/(b*n) - p)/2, -p, (2 - (2*I)/(b*n) - p)/2, E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Sin[a + b*Log[c*x^n]]^p)/((2 - I*b*n*p)*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^p)","A",3,3,15,0.2000,1,"{4493, 4491, 364}"
82,1,112,0,0.0747292,"\int \sin ^p\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sin[a + b*Log[c*x^n]]^p,x]","\frac{x \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{-p} \, _2F_1\left(-p,-\frac{b n p+i}{2 b n};\frac{1}{2} \left(-p-\frac{i}{b n}+2\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sin ^p\left(a+b \log \left(c x^n\right)\right)}{1-i b n p}","\frac{x \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{-p} \, _2F_1\left(-p,-\frac{b n p+i}{2 b n};\frac{1}{2} \left(-p-\frac{i}{b n}+2\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sin ^p\left(a+b \log \left(c x^n\right)\right)}{1-i b n p}",1,"(x*Hypergeometric2F1[-p, -(I + b*n*p)/(2*b*n), (2 - I/(b*n) - p)/2, E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Sin[a + b*Log[c*x^n]]^p)/((1 - I*b*n*p)*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^p)","A",3,3,13,0.2308,1,"{4483, 4491, 364}"
83,1,86,0,0.0601127,"\int \frac{\sin ^p\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Sin[a + b*Log[c*x^n]]^p/x,x]","\frac{\cos \left(a+b \log \left(c x^n\right)\right) \sin ^{p+1}\left(a+b \log \left(c x^n\right)\right) \, _2F_1\left(\frac{1}{2},\frac{p+1}{2};\frac{p+3}{2};\sin ^2\left(a+b \log \left(c x^n\right)\right)\right)}{b n (p+1) \sqrt{\cos ^2\left(a+b \log \left(c x^n\right)\right)}}","\frac{\cos \left(a+b \log \left(c x^n\right)\right) \sin ^{p+1}\left(a+b \log \left(c x^n\right)\right) \, _2F_1\left(\frac{1}{2},\frac{p+1}{2};\frac{p+3}{2};\sin ^2\left(a+b \log \left(c x^n\right)\right)\right)}{b n (p+1) \sqrt{\cos ^2\left(a+b \log \left(c x^n\right)\right)}}",1,"(Cos[a + b*Log[c*x^n]]*Hypergeometric2F1[1/2, (1 + p)/2, (3 + p)/2, Sin[a + b*Log[c*x^n]]^2]*Sin[a + b*Log[c*x^n]]^(1 + p))/(b*n*(1 + p)*Sqrt[Cos[a + b*Log[c*x^n]]^2])","A",2,1,17,0.05882,1,"{2643}"
84,1,115,0,0.0948704,"\int \frac{\sin ^p\left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[Sin[a + b*Log[c*x^n]]^p/x^2,x]","-\frac{\left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{-p} \, _2F_1\left(\frac{1}{2} \left(\frac{i}{b n}-p\right),-p;\frac{1}{2} \left(-p+\frac{i}{b n}+2\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sin ^p\left(a+b \log \left(c x^n\right)\right)}{x (1+i b n p)}","-\frac{\left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{-p} \, _2F_1\left(\frac{1}{2} \left(\frac{i}{b n}-p\right),-p;\frac{1}{2} \left(-p+\frac{i}{b n}+2\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sin ^p\left(a+b \log \left(c x^n\right)\right)}{x (1+i b n p)}",1,"-((Hypergeometric2F1[(I/(b*n) - p)/2, -p, (2 + I/(b*n) - p)/2, E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Sin[a + b*Log[c*x^n]]^p)/((1 + I*b*n*p)*x*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^p))","A",3,3,17,0.1765,1,"{4493, 4491, 364}"
85,1,115,0,0.0924682,"\int \frac{\sin ^p\left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[Sin[a + b*Log[c*x^n]]^p/x^3,x]","-\frac{\left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{-p} \, _2F_1\left(\frac{1}{2} \left(\frac{2 i}{b n}-p\right),-p;\frac{1}{2} \left(-p+\frac{2 i}{b n}+2\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sin ^p\left(a+b \log \left(c x^n\right)\right)}{x^2 (2+i b n p)}","-\frac{\left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{-p} \, _2F_1\left(\frac{1}{2} \left(\frac{2 i}{b n}-p\right),-p;\frac{1}{2} \left(-p+\frac{2 i}{b n}+2\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sin ^p\left(a+b \log \left(c x^n\right)\right)}{x^2 (2+i b n p)}",1,"-((Hypergeometric2F1[((2*I)/(b*n) - p)/2, -p, (2 + (2*I)/(b*n) - p)/2, E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Sin[a + b*Log[c*x^n]]^p)/((2 + I*b*n*p)*x^2*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^p))","A",3,3,17,0.1765,1,"{4493, 4491, 364}"
86,1,56,0,0.0175289,"\int x^2 \cos \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*Cos[a + b*Log[c*x^n]],x]","\frac{b n x^3 \sin \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+9}+\frac{3 x^3 \cos \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+9}","\frac{b n x^3 \sin \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+9}+\frac{3 x^3 \cos \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+9}",1,"(3*x^3*Cos[a + b*Log[c*x^n]])/(9 + b^2*n^2) + (b*n*x^3*Sin[a + b*Log[c*x^n]])/(9 + b^2*n^2)","A",1,1,15,0.06667,1,"{4486}"
87,1,56,0,0.0118961,"\int x \cos \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Cos[a + b*Log[c*x^n]],x]","\frac{b n x^2 \sin \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+4}+\frac{2 x^2 \cos \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+4}","\frac{b n x^2 \sin \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+4}+\frac{2 x^2 \cos \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+4}",1,"(2*x^2*Cos[a + b*Log[c*x^n]])/(4 + b^2*n^2) + (b*n*x^2*Sin[a + b*Log[c*x^n]])/(4 + b^2*n^2)","A",1,1,13,0.07692,1,"{4486}"
88,1,51,0,0.0091753,"\int \cos \left(a+b \log \left(c x^n\right)\right) \, dx","Int[Cos[a + b*Log[c*x^n]],x]","\frac{b n x \sin \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+1}+\frac{x \cos \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+1}","\frac{b n x \sin \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+1}+\frac{x \cos \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+1}",1,"(x*Cos[a + b*Log[c*x^n]])/(1 + b^2*n^2) + (b*n*x*Sin[a + b*Log[c*x^n]])/(1 + b^2*n^2)","A",1,1,11,0.09091,1,"{4476}"
89,1,18,0,0.0147802,"\int \frac{\cos \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Cos[a + b*Log[c*x^n]]/x,x]","\frac{\sin \left(a+b \log \left(c x^n\right)\right)}{b n}","\frac{\sin \left(a+b \log \left(c x^n\right)\right)}{b n}",1,"Sin[a + b*Log[c*x^n]]/(b*n)","A",2,1,15,0.06667,1,"{2637}"
90,1,56,0,0.015031,"\int \frac{\cos \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[Cos[a + b*Log[c*x^n]]/x^2,x]","\frac{b n \sin \left(a+b \log \left(c x^n\right)\right)}{x \left(b^2 n^2+1\right)}-\frac{\cos \left(a+b \log \left(c x^n\right)\right)}{x \left(b^2 n^2+1\right)}","\frac{b n \sin \left(a+b \log \left(c x^n\right)\right)}{x \left(b^2 n^2+1\right)}-\frac{\cos \left(a+b \log \left(c x^n\right)\right)}{x \left(b^2 n^2+1\right)}",1,"-(Cos[a + b*Log[c*x^n]]/((1 + b^2*n^2)*x)) + (b*n*Sin[a + b*Log[c*x^n]])/((1 + b^2*n^2)*x)","A",1,1,15,0.06667,1,"{4486}"
91,1,97,0,0.0300538,"\int x^2 \cos ^2\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*Cos[a + b*Log[c*x^n]]^2,x]","\frac{3 x^3 \cos ^2\left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+9}+\frac{2 b n x^3 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+9}+\frac{2 b^2 n^2 x^3}{3 \left(4 b^2 n^2+9\right)}","\frac{3 x^3 \cos ^2\left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+9}+\frac{2 b n x^3 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+9}+\frac{2 b^2 n^2 x^3}{3 \left(4 b^2 n^2+9\right)}",1,"(2*b^2*n^2*x^3)/(3*(9 + 4*b^2*n^2)) + (3*x^3*Cos[a + b*Log[c*x^n]]^2)/(9 + 4*b^2*n^2) + (2*b*n*x^3*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/(9 + 4*b^2*n^2)","A",2,2,17,0.1176,1,"{4488, 30}"
92,1,98,0,0.0231482,"\int x \cos ^2\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Cos[a + b*Log[c*x^n]]^2,x]","\frac{x^2 \cos ^2\left(a+b \log \left(c x^n\right)\right)}{2 \left(b^2 n^2+1\right)}+\frac{b n x^2 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{2 \left(b^2 n^2+1\right)}+\frac{b^2 n^2 x^2}{4 \left(b^2 n^2+1\right)}","\frac{x^2 \cos ^2\left(a+b \log \left(c x^n\right)\right)}{2 \left(b^2 n^2+1\right)}+\frac{b n x^2 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{2 \left(b^2 n^2+1\right)}+\frac{b^2 n^2 x^2}{4 \left(b^2 n^2+1\right)}",1,"(b^2*n^2*x^2)/(4*(1 + b^2*n^2)) + (x^2*Cos[a + b*Log[c*x^n]]^2)/(2*(1 + b^2*n^2)) + (b*n*x^2*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/(2*(1 + b^2*n^2))","A",2,2,15,0.1333,1,"{4488, 30}"
93,1,88,0,0.0162598,"\int \cos ^2\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Cos[a + b*Log[c*x^n]]^2,x]","\frac{x \cos ^2\left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+1}+\frac{2 b n x \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+1}+\frac{2 b^2 n^2 x}{4 b^2 n^2+1}","\frac{x \cos ^2\left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+1}+\frac{2 b n x \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+1}+\frac{2 b^2 n^2 x}{4 b^2 n^2+1}",1,"(2*b^2*n^2*x)/(1 + 4*b^2*n^2) + (x*Cos[a + b*Log[c*x^n]]^2)/(1 + 4*b^2*n^2) + (2*b*n*x*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/(1 + 4*b^2*n^2)","A",2,2,13,0.1538,1,"{4478, 8}"
94,1,39,0,0.0288512,"\int \frac{\cos ^2\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Cos[a + b*Log[c*x^n]]^2/x,x]","\frac{\sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{2 b n}+\frac{\log (x)}{2}","\frac{\sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{2 b n}+\frac{\log (x)}{2}",1,"Log[x]/2 + (Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/(2*b*n)","A",3,2,17,0.1176,1,"{2635, 8}"
95,1,95,0,0.026947,"\int \frac{\cos ^2\left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[Cos[a + b*Log[c*x^n]]^2/x^2,x]","-\frac{\cos ^2\left(a+b \log \left(c x^n\right)\right)}{x \left(4 b^2 n^2+1\right)}+\frac{2 b n \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{x \left(4 b^2 n^2+1\right)}-\frac{2 b^2 n^2}{x \left(4 b^2 n^2+1\right)}","-\frac{\cos ^2\left(a+b \log \left(c x^n\right)\right)}{x \left(4 b^2 n^2+1\right)}+\frac{2 b n \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{x \left(4 b^2 n^2+1\right)}-\frac{2 b^2 n^2}{x \left(4 b^2 n^2+1\right)}",1,"(-2*b^2*n^2)/((1 + 4*b^2*n^2)*x) - Cos[a + b*Log[c*x^n]]^2/((1 + 4*b^2*n^2)*x) + (2*b*n*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/((1 + 4*b^2*n^2)*x)","A",2,2,17,0.1176,1,"{4488, 30}"
96,1,160,0,0.0511728,"\int x^2 \cos ^3\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*Cos[a + b*Log[c*x^n]]^3,x]","\frac{2 b^3 n^3 x^3 \sin \left(a+b \log \left(c x^n\right)\right)}{3 \left(b^4 n^4+10 b^2 n^2+9\right)}+\frac{x^3 \cos ^3\left(a+b \log \left(c x^n\right)\right)}{3 \left(b^2 n^2+1\right)}+\frac{2 b^2 n^2 x^3 \cos \left(a+b \log \left(c x^n\right)\right)}{b^4 n^4+10 b^2 n^2+9}+\frac{b n x^3 \sin \left(a+b \log \left(c x^n\right)\right) \cos ^2\left(a+b \log \left(c x^n\right)\right)}{3 \left(b^2 n^2+1\right)}","\frac{2 b^3 n^3 x^3 \sin \left(a+b \log \left(c x^n\right)\right)}{3 \left(b^4 n^4+10 b^2 n^2+9\right)}+\frac{x^3 \cos ^3\left(a+b \log \left(c x^n\right)\right)}{3 \left(b^2 n^2+1\right)}+\frac{2 b^2 n^2 x^3 \cos \left(a+b \log \left(c x^n\right)\right)}{b^4 n^4+10 b^2 n^2+9}+\frac{b n x^3 \sin \left(a+b \log \left(c x^n\right)\right) \cos ^2\left(a+b \log \left(c x^n\right)\right)}{3 \left(b^2 n^2+1\right)}",1,"(2*b^2*n^2*x^3*Cos[a + b*Log[c*x^n]])/(9 + 10*b^2*n^2 + b^4*n^4) + (x^3*Cos[a + b*Log[c*x^n]]^3)/(3*(1 + b^2*n^2)) + (2*b^3*n^3*x^3*Sin[a + b*Log[c*x^n]])/(3*(9 + 10*b^2*n^2 + b^4*n^4)) + (b*n*x^3*Cos[a + b*Log[c*x^n]]^2*Sin[a + b*Log[c*x^n]])/(3*(1 + b^2*n^2))","A",2,2,17,0.1176,1,"{4488, 4486}"
97,1,158,0,0.0451337,"\int x \cos ^3\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Cos[a + b*Log[c*x^n]]^3,x]","\frac{6 b^3 n^3 x^2 \sin \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4+40 b^2 n^2+16}+\frac{2 x^2 \cos ^3\left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+4}+\frac{12 b^2 n^2 x^2 \cos \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4+40 b^2 n^2+16}+\frac{3 b n x^2 \sin \left(a+b \log \left(c x^n\right)\right) \cos ^2\left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+4}","\frac{6 b^3 n^3 x^2 \sin \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4+40 b^2 n^2+16}+\frac{2 x^2 \cos ^3\left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+4}+\frac{12 b^2 n^2 x^2 \cos \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4+40 b^2 n^2+16}+\frac{3 b n x^2 \sin \left(a+b \log \left(c x^n\right)\right) \cos ^2\left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+4}",1,"(12*b^2*n^2*x^2*Cos[a + b*Log[c*x^n]])/(16 + 40*b^2*n^2 + 9*b^4*n^4) + (2*x^2*Cos[a + b*Log[c*x^n]]^3)/(4 + 9*b^2*n^2) + (6*b^3*n^3*x^2*Sin[a + b*Log[c*x^n]])/(16 + 40*b^2*n^2 + 9*b^4*n^4) + (3*b*n*x^2*Cos[a + b*Log[c*x^n]]^2*Sin[a + b*Log[c*x^n]])/(4 + 9*b^2*n^2)","A",2,2,15,0.1333,1,"{4488, 4486}"
98,1,149,0,0.036033,"\int \cos ^3\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Cos[a + b*Log[c*x^n]]^3,x]","\frac{6 b^3 n^3 x \sin \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4+10 b^2 n^2+1}+\frac{x \cos ^3\left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+1}+\frac{6 b^2 n^2 x \cos \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4+10 b^2 n^2+1}+\frac{3 b n x \sin \left(a+b \log \left(c x^n\right)\right) \cos ^2\left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+1}","\frac{6 b^3 n^3 x \sin \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4+10 b^2 n^2+1}+\frac{x \cos ^3\left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+1}+\frac{6 b^2 n^2 x \cos \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4+10 b^2 n^2+1}+\frac{3 b n x \sin \left(a+b \log \left(c x^n\right)\right) \cos ^2\left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+1}",1,"(6*b^2*n^2*x*Cos[a + b*Log[c*x^n]])/(1 + 10*b^2*n^2 + 9*b^4*n^4) + (x*Cos[a + b*Log[c*x^n]]^3)/(1 + 9*b^2*n^2) + (6*b^3*n^3*x*Sin[a + b*Log[c*x^n]])/(1 + 10*b^2*n^2 + 9*b^4*n^4) + (3*b*n*x*Cos[a + b*Log[c*x^n]]^2*Sin[a + b*Log[c*x^n]])/(1 + 9*b^2*n^2)","A",2,2,13,0.1538,1,"{4478, 4476}"
99,1,42,0,0.032968,"\int \frac{\cos ^3\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Cos[a + b*Log[c*x^n]]^3/x,x]","\frac{\sin \left(a+b \log \left(c x^n\right)\right)}{b n}-\frac{\sin ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}","\frac{\sin \left(a+b \log \left(c x^n\right)\right)}{b n}-\frac{\sin ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}",1,"Sin[a + b*Log[c*x^n]]/(b*n) - Sin[a + b*Log[c*x^n]]^3/(3*b*n)","A",3,1,17,0.05882,1,"{2633}"
100,1,158,0,0.0482041,"\int \frac{\cos ^3\left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[Cos[a + b*Log[c*x^n]]^3/x^2,x]","\frac{6 b^3 n^3 \sin \left(a+b \log \left(c x^n\right)\right)}{x \left(9 b^4 n^4+10 b^2 n^2+1\right)}-\frac{\cos ^3\left(a+b \log \left(c x^n\right)\right)}{x \left(9 b^2 n^2+1\right)}-\frac{6 b^2 n^2 \cos \left(a+b \log \left(c x^n\right)\right)}{x \left(9 b^4 n^4+10 b^2 n^2+1\right)}+\frac{3 b n \sin \left(a+b \log \left(c x^n\right)\right) \cos ^2\left(a+b \log \left(c x^n\right)\right)}{x \left(9 b^2 n^2+1\right)}","\frac{6 b^3 n^3 \sin \left(a+b \log \left(c x^n\right)\right)}{x \left(9 b^4 n^4+10 b^2 n^2+1\right)}-\frac{\cos ^3\left(a+b \log \left(c x^n\right)\right)}{x \left(9 b^2 n^2+1\right)}-\frac{6 b^2 n^2 \cos \left(a+b \log \left(c x^n\right)\right)}{x \left(9 b^4 n^4+10 b^2 n^2+1\right)}+\frac{3 b n \sin \left(a+b \log \left(c x^n\right)\right) \cos ^2\left(a+b \log \left(c x^n\right)\right)}{x \left(9 b^2 n^2+1\right)}",1,"(-6*b^2*n^2*Cos[a + b*Log[c*x^n]])/((1 + 10*b^2*n^2 + 9*b^4*n^4)*x) - Cos[a + b*Log[c*x^n]]^3/((1 + 9*b^2*n^2)*x) + (6*b^3*n^3*Sin[a + b*Log[c*x^n]])/((1 + 10*b^2*n^2 + 9*b^4*n^4)*x) + (3*b*n*Cos[a + b*Log[c*x^n]]^2*Sin[a + b*Log[c*x^n]])/((1 + 9*b^2*n^2)*x)","A",2,2,17,0.1176,1,"{4488, 4486}"
101,1,191,0,0.0449368,"\int \cos ^4\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Cos[a + b*Log[c*x^n]]^4,x]","\frac{12 b^2 n^2 x \cos ^2\left(a+b \log \left(c x^n\right)\right)}{64 b^4 n^4+20 b^2 n^2+1}+\frac{x \cos ^4\left(a+b \log \left(c x^n\right)\right)}{16 b^2 n^2+1}+\frac{4 b n x \sin \left(a+b \log \left(c x^n\right)\right) \cos ^3\left(a+b \log \left(c x^n\right)\right)}{16 b^2 n^2+1}+\frac{24 b^3 n^3 x \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{64 b^4 n^4+20 b^2 n^2+1}+\frac{24 b^4 n^4 x}{64 b^4 n^4+20 b^2 n^2+1}","\frac{12 b^2 n^2 x \cos ^2\left(a+b \log \left(c x^n\right)\right)}{64 b^4 n^4+20 b^2 n^2+1}+\frac{x \cos ^4\left(a+b \log \left(c x^n\right)\right)}{16 b^2 n^2+1}+\frac{4 b n x \sin \left(a+b \log \left(c x^n\right)\right) \cos ^3\left(a+b \log \left(c x^n\right)\right)}{16 b^2 n^2+1}+\frac{24 b^3 n^3 x \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{64 b^4 n^4+20 b^2 n^2+1}+\frac{24 b^4 n^4 x}{64 b^4 n^4+20 b^2 n^2+1}",1,"(24*b^4*n^4*x)/(1 + 20*b^2*n^2 + 64*b^4*n^4) + (12*b^2*n^2*x*Cos[a + b*Log[c*x^n]]^2)/(1 + 20*b^2*n^2 + 64*b^4*n^4) + (x*Cos[a + b*Log[c*x^n]]^4)/(1 + 16*b^2*n^2) + (24*b^3*n^3*x*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/(1 + 20*b^2*n^2 + 64*b^4*n^4) + (4*b*n*x*Cos[a + b*Log[c*x^n]]^3*Sin[a + b*Log[c*x^n]])/(1 + 16*b^2*n^2)","A",3,2,13,0.1538,1,"{4478, 8}"
102,1,73,0,0.0441463,"\int \frac{\cos ^4\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Cos[a + b*Log[c*x^n]]^4/x,x]","\frac{\sin \left(a+b \log \left(c x^n\right)\right) \cos ^3\left(a+b \log \left(c x^n\right)\right)}{4 b n}+\frac{3 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{8 b n}+\frac{3 \log (x)}{8}","\frac{\sin \left(a+b \log \left(c x^n\right)\right) \cos ^3\left(a+b \log \left(c x^n\right)\right)}{4 b n}+\frac{3 \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{8 b n}+\frac{3 \log (x)}{8}",1,"(3*Log[x])/8 + (3*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/(8*b*n) + (Cos[a + b*Log[c*x^n]]^3*Sin[a + b*Log[c*x^n]])/(4*b*n)","A",4,2,17,0.1176,1,"{2635, 8}"
103,1,29,0,0.0137795,"\int \cos (\log (6+3 x)) \, dx","Int[Cos[Log[6 + 3*x]],x]","\frac{1}{2} (x+2) \sin (\log (3 (x+2)))+\frac{1}{2} (x+2) \cos (\log (3 (x+2)))","\frac{1}{2} (x+2) \sin (\log (3 (x+2)))+\frac{1}{2} (x+2) \cos (\log (3 (x+2)))",1,"((2 + x)*Cos[Log[3*(2 + x)]])/2 + ((2 + x)*Sin[Log[3*(2 + x)]])/2","A",2,1,7,0.1429,1,"{4476}"
104,1,101,0,0.1456087,"\int x^m \cos \left(a+\sqrt{-\frac{(1+m)^2}{n^2}} \log \left(c x^n\right)\right) \, dx","Int[x^m*Cos[a + Sqrt[-((1 + m)^2/n^2)]*Log[c*x^n]],x]","\frac{x^{m+1} e^{\frac{a (m+1)}{n \sqrt{-\frac{(m+1)^2}{n^2}}}} \left(c x^n\right)^{\frac{m+1}{n}}}{4 (m+1)}+\frac{1}{2} x^{m+1} \log (x) e^{\frac{a n \sqrt{-\frac{(m+1)^2}{n^2}}}{m+1}} \left(c x^n\right)^{-\frac{m+1}{n}}","\frac{x^{m+1} e^{\frac{a (m+1)}{n \sqrt{-\frac{(m+1)^2}{n^2}}}} \left(c x^n\right)^{\frac{m+1}{n}}}{4 (m+1)}+\frac{1}{2} x^{m+1} \log (x) e^{\frac{a n \sqrt{-\frac{(m+1)^2}{n^2}}}{m+1}} \left(c x^n\right)^{-\frac{m+1}{n}}",1,"(E^((a*(1 + m))/(Sqrt[-((1 + m)^2/n^2)]*n))*x^(1 + m)*(c*x^n)^((1 + m)/n))/(4*(1 + m)) + (E^((a*Sqrt[-((1 + m)^2/n^2)]*n)/(1 + m))*x^(1 + m)*Log[x])/(2*(c*x^n)^((1 + m)/n))","A",3,2,28,0.07143,1,"{4494, 4490}"
105,1,62,0,0.0448417,"\int \cos \left(a+\sqrt{-\frac{1}{n^2}} \log \left(c x^n\right)\right) \, dx","Int[Cos[a + Sqrt[-n^(-2)]*Log[c*x^n]],x]","\frac{1}{4} x e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\frac{1}{n}}+\frac{1}{2} x e^{a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-1/n}","\frac{1}{4} x e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\frac{1}{n}}+\frac{1}{2} x e^{a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-1/n}",1,"(x*(c*x^n)^n^(-1))/(4*E^(a*Sqrt[-n^(-2)]*n)) + (E^(a*Sqrt[-n^(-2)]*n)*x*Log[x])/(2*(c*x^n)^n^(-1))","A",3,2,19,0.1053,1,"{4484, 4490}"
106,1,117,0,0.1172123,"\int x^m \cos ^2\left(a+\frac{1}{2} \sqrt{-\frac{(1+m)^2}{n^2}} \log \left(c x^n\right)\right) \, dx","Int[x^m*Cos[a + (Sqrt[-((1 + m)^2/n^2)]*Log[c*x^n])/2]^2,x]","\frac{x^{m+1} e^{-\frac{2 a n \sqrt{-\frac{(m+1)^2}{n^2}}}{m+1}} \left(c x^n\right)^{\frac{m+1}{n}}}{8 (m+1)}+\frac{1}{4} x^{m+1} \log (x) e^{\frac{2 a n \sqrt{-\frac{(m+1)^2}{n^2}}}{m+1}} \left(c x^n\right)^{-\frac{m+1}{n}}+\frac{x^{m+1}}{2 (m+1)}","\frac{x^{m+1} e^{-\frac{2 a n \sqrt{-\frac{(m+1)^2}{n^2}}}{m+1}} \left(c x^n\right)^{\frac{m+1}{n}}}{8 (m+1)}+\frac{1}{4} x^{m+1} \log (x) e^{\frac{2 a n \sqrt{-\frac{(m+1)^2}{n^2}}}{m+1}} \left(c x^n\right)^{-\frac{m+1}{n}}+\frac{x^{m+1}}{2 (m+1)}",1,"x^(1 + m)/(2*(1 + m)) + (x^(1 + m)*(c*x^n)^((1 + m)/n))/(8*E^((2*a*Sqrt[-((1 + m)^2/n^2)]*n)/(1 + m))*(1 + m)) + (E^((2*a*Sqrt[-((1 + m)^2/n^2)]*n)/(1 + m))*x^(1 + m)*Log[x])/(4*(c*x^n)^((1 + m)/n))","A",3,2,33,0.06061,1,"{4494, 4490}"
107,1,68,0,0.0557935,"\int \cos ^2\left(a+\frac{1}{2} \sqrt{-\frac{1}{n^2}} \log \left(c x^n\right)\right) \, dx","Int[Cos[a + (Sqrt[-n^(-2)]*Log[c*x^n])/2]^2,x]","\frac{1}{8} x e^{-2 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\frac{1}{n}}+\frac{1}{4} x e^{2 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-1/n}+\frac{x}{2}","\frac{1}{8} x e^{-2 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\frac{1}{n}}+\frac{1}{4} x e^{2 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-1/n}+\frac{x}{2}",1,"x/2 + (x*(c*x^n)^n^(-1))/(8*E^(2*a*Sqrt[-n^(-2)]*n)) + (E^(2*a*Sqrt[-n^(-2)]*n)*x*Log[x])/(4*(c*x^n)^n^(-1))","A",3,2,24,0.08333,1,"{4484, 4490}"
108,1,226,0,0.0817879,"\int x^m \cos ^3\left(a+\frac{1}{2} \sqrt{-\frac{(1+m)^2}{n^2}} \log \left(c x^n\right)\right) \, dx","Int[x^m*Cos[a + (Sqrt[-((1 + m)^2/n^2)]*Log[c*x^n])/2]^3,x]","\frac{4 n \sqrt{-\frac{(m+1)^2}{n^2}} x^{m+1} \sin \left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right)}{5 (m+1)^2}-\frac{4 x^{m+1} \cos ^3\left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right)}{5 (m+1)}+\frac{8 x^{m+1} \cos \left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right)}{5 (m+1)}-\frac{6 n \sqrt{-\frac{(m+1)^2}{n^2}} x^{m+1} \sin \left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right) \cos ^2\left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right)}{5 (m+1)^2}","\frac{4 n \sqrt{-\frac{(m+1)^2}{n^2}} x^{m+1} \sin \left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right)}{5 (m+1)^2}-\frac{4 x^{m+1} \cos ^3\left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right)}{5 (m+1)}+\frac{8 x^{m+1} \cos \left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right)}{5 (m+1)}-\frac{6 n \sqrt{-\frac{(m+1)^2}{n^2}} x^{m+1} \sin \left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right) \cos ^2\left(a+\frac{1}{2} \sqrt{-\frac{(m+1)^2}{n^2}} \log \left(c x^n\right)\right)}{5 (m+1)^2}",1,"(8*x^(1 + m)*Cos[a + (Sqrt[-((1 + m)^2/n^2)]*Log[c*x^n])/2])/(5*(1 + m)) - (4*x^(1 + m)*Cos[a + (Sqrt[-((1 + m)^2/n^2)]*Log[c*x^n])/2]^3)/(5*(1 + m)) + (4*Sqrt[-((1 + m)^2/n^2)]*n*x^(1 + m)*Sin[a + (Sqrt[-((1 + m)^2/n^2)]*Log[c*x^n])/2])/(5*(1 + m)^2) - (6*Sqrt[-((1 + m)^2/n^2)]*n*x^(1 + m)*Cos[a + (Sqrt[-((1 + m)^2/n^2)]*Log[c*x^n])/2]^2*Sin[a + (Sqrt[-((1 + m)^2/n^2)]*Log[c*x^n])/2])/(5*(1 + m)^2)","A",2,2,33,0.06061,1,"{4488, 4486}"
109,1,128,0,0.0958812,"\int \cos ^3\left(a+\frac{1}{3} \sqrt{-\frac{1}{n^2}} \log \left(c x^n\right)\right) \, dx","Int[Cos[a + (Sqrt[-n^(-2)]*Log[c*x^n])/3]^3,x]","\frac{9}{16} x e^{a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.-\frac{1}{3}\right/n}+\frac{9}{32} x e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.\frac{1}{3}\right/n}+\frac{1}{16} x e^{-3 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\frac{1}{n}}+\frac{1}{8} x e^{3 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-1/n}","\frac{9}{16} x e^{a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.-\frac{1}{3}\right/n}+\frac{9}{32} x e^{-a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\left.\frac{1}{3}\right/n}+\frac{1}{16} x e^{-3 a \sqrt{-\frac{1}{n^2}} n} \left(c x^n\right)^{\frac{1}{n}}+\frac{1}{8} x e^{3 a \sqrt{-\frac{1}{n^2}} n} \log (x) \left(c x^n\right)^{-1/n}",1,"(9*E^(a*Sqrt[-n^(-2)]*n)*x)/(16*(c*x^n)^(1/(3*n))) + (9*x*(c*x^n)^(1/(3*n)))/(32*E^(a*Sqrt[-n^(-2)]*n)) + (x*(c*x^n)^n^(-1))/(16*E^(3*a*Sqrt[-n^(-2)]*n)) + (E^(3*a*Sqrt[-n^(-2)]*n)*x*Log[x])/(8*(c*x^n)^n^(-1))","A",3,2,24,0.08333,1,"{4484, 4490}"
110,1,110,0,0.0715192,"\int \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)} \, dx","Int[Sqrt[Cos[a + b*Log[c*x^n]]],x]","\frac{2 x \, _2F_1\left(-\frac{1}{2},-\frac{b n+2 i}{4 b n};\frac{1}{4} \left(3-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)}}{(2-i b n) \sqrt{1+e^{2 i a} \left(c x^n\right)^{2 i b}}}","\frac{2 x \, _2F_1\left(-\frac{1}{2},-\frac{b n+2 i}{4 b n};\frac{1}{4} \left(3-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)}}{(2-i b n) \sqrt{1+e^{2 i a} \left(c x^n\right)^{2 i b}}}",1,"(2*x*Sqrt[Cos[a + b*Log[c*x^n]]]*Hypergeometric2F1[-1/2, -(2*I + b*n)/(4*b*n), (3 - (2*I)/(b*n))/4, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((2 - I*b*n)*Sqrt[1 + E^((2*I)*a)*(c*x^n)^((2*I)*b)])","A",3,3,15,0.2000,1,"{4484, 4492, 364}"
111,1,24,0,0.0269538,"\int \frac{\sqrt{\cos \left(a+b \log \left(c x^n\right)\right)}}{x} \, dx","Int[Sqrt[Cos[a + b*Log[c*x^n]]]/x,x]","\frac{2 E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}","\frac{2 E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}",1,"(2*EllipticE[(a + b*Log[c*x^n])/2, 2])/(b*n)","A",2,1,19,0.05263,1,"{2639}"
112,1,109,0,0.0678703,"\int \cos ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Cos[a + b*Log[c*x^n]]^(3/2),x]","\frac{2 x \, _2F_1\left(-\frac{3}{2},\frac{1}{4} \left(-3-\frac{2 i}{b n}\right);\frac{1}{4} \left(1-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \cos ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{(2-3 i b n) \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2}}","\frac{2 x \, _2F_1\left(-\frac{3}{2},\frac{1}{4} \left(-3-\frac{2 i}{b n}\right);\frac{1}{4} \left(1-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \cos ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{(2-3 i b n) \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2}}",1,"(2*x*Cos[a + b*Log[c*x^n]]^(3/2)*Hypergeometric2F1[-3/2, (-3 - (2*I)/(b*n))/4, (1 - (2*I)/(b*n))/4, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((2 - (3*I)*b*n)*(1 + E^((2*I)*a)*(c*x^n)^((2*I)*b))^(3/2))","A",3,3,15,0.2000,1,"{4484, 4492, 364}"
113,1,63,0,0.0426202,"\int \frac{\cos ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Cos[a + b*Log[c*x^n]]^(3/2)/x,x]","\frac{2 F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{3 b n}+\frac{2 \sin \left(a+b \log \left(c x^n\right)\right) \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)}}{3 b n}","\frac{2 F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{3 b n}+\frac{2 \sin \left(a+b \log \left(c x^n\right)\right) \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)}}{3 b n}",1,"(2*EllipticF[(a + b*Log[c*x^n])/2, 2])/(3*b*n) + (2*Sqrt[Cos[a + b*Log[c*x^n]]]*Sin[a + b*Log[c*x^n]])/(3*b*n)","A",3,2,19,0.1053,1,"{2635, 2641}"
114,1,110,0,0.0718108,"\int \cos ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Cos[a + b*Log[c*x^n]]^(5/2),x]","\frac{2 x \, _2F_1\left(-\frac{5}{2},\frac{1}{4} \left(-5-\frac{2 i}{b n}\right);-\frac{b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \cos ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{(2-5 i b n) \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2}}","\frac{2 x \, _2F_1\left(-\frac{5}{2},\frac{1}{4} \left(-5-\frac{2 i}{b n}\right);-\frac{b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \cos ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{(2-5 i b n) \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2}}",1,"(2*x*Cos[a + b*Log[c*x^n]]^(5/2)*Hypergeometric2F1[-5/2, (-5 - (2*I)/(b*n))/4, -(2*I + b*n)/(4*b*n), -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((2 - (5*I)*b*n)*(1 + E^((2*I)*a)*(c*x^n)^((2*I)*b))^(5/2))","A",3,3,15,0.2000,1,"{4484, 4492, 364}"
115,1,63,0,0.0423989,"\int \frac{\cos ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Cos[a + b*Log[c*x^n]]^(5/2)/x,x]","\frac{6 E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{5 b n}+\frac{2 \sin \left(a+b \log \left(c x^n\right)\right) \cos ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{5 b n}","\frac{6 E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{5 b n}+\frac{2 \sin \left(a+b \log \left(c x^n\right)\right) \cos ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{5 b n}",1,"(6*EllipticE[(a + b*Log[c*x^n])/2, 2])/(5*b*n) + (2*Cos[a + b*Log[c*x^n]]^(3/2)*Sin[a + b*Log[c*x^n]])/(5*b*n)","A",3,2,19,0.1053,1,"{2635, 2639}"
116,1,109,0,0.0667546,"\int \frac{1}{\sqrt{\cos \left(a+b \log \left(c x^n\right)\right)}} \, dx","Int[1/Sqrt[Cos[a + b*Log[c*x^n]]],x]","\frac{2 x \sqrt{1+e^{2 i a} \left(c x^n\right)^{2 i b}} \, _2F_1\left(\frac{1}{2},\frac{1}{4} \left(1-\frac{2 i}{b n}\right);\frac{1}{4} \left(5-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2+i b n) \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)}}","\frac{2 x \sqrt{1+e^{2 i a} \left(c x^n\right)^{2 i b}} \, _2F_1\left(\frac{1}{2},\frac{1}{4} \left(1-\frac{2 i}{b n}\right);\frac{1}{4} \left(5-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2+i b n) \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)}}",1,"(2*x*Sqrt[1 + E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Hypergeometric2F1[1/2, (1 - (2*I)/(b*n))/4, (5 - (2*I)/(b*n))/4, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((2 + I*b*n)*Sqrt[Cos[a + b*Log[c*x^n]]])","A",3,3,15,0.2000,1,"{4484, 4492, 364}"
117,1,24,0,0.0279455,"\int \frac{1}{x \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)}} \, dx","Int[1/(x*Sqrt[Cos[a + b*Log[c*x^n]]]),x]","\frac{2 F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}","\frac{2 F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}",1,"(2*EllipticF[(a + b*Log[c*x^n])/2, 2])/(b*n)","A",2,1,19,0.05263,1,"{2641}"
118,1,109,0,0.0698297,"\int \frac{1}{\cos ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[Cos[a + b*Log[c*x^n]]^(-3/2),x]","\frac{2 x \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{1}{4} \left(3-\frac{2 i}{b n}\right);\frac{1}{4} \left(7-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2+3 i b n) \cos ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}","\frac{2 x \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{1}{4} \left(3-\frac{2 i}{b n}\right);\frac{1}{4} \left(7-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2+3 i b n) \cos ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}",1,"(2*x*(1 + E^((2*I)*a)*(c*x^n)^((2*I)*b))^(3/2)*Hypergeometric2F1[3/2, (3 - (2*I)/(b*n))/4, (7 - (2*I)/(b*n))/4, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((2 + (3*I)*b*n)*Cos[a + b*Log[c*x^n]]^(3/2))","A",3,3,15,0.2000,1,"{4484, 4492, 364}"
119,1,59,0,0.0410599,"\int \frac{1}{x \cos ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[1/(x*Cos[a + b*Log[c*x^n]]^(3/2)),x]","\frac{2 \sin \left(a+b \log \left(c x^n\right)\right)}{b n \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)}}-\frac{2 E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}","\frac{2 \sin \left(a+b \log \left(c x^n\right)\right)}{b n \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)}}-\frac{2 E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}",1,"(-2*EllipticE[(a + b*Log[c*x^n])/2, 2])/(b*n) + (2*Sin[a + b*Log[c*x^n]])/(b*n*Sqrt[Cos[a + b*Log[c*x^n]]])","A",3,2,19,0.1053,1,"{2636, 2639}"
120,1,109,0,0.0728147,"\int \frac{1}{\cos ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[Cos[a + b*Log[c*x^n]]^(-5/2),x]","\frac{2 x \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2} \, _2F_1\left(\frac{5}{2},\frac{1}{4} \left(5-\frac{2 i}{b n}\right);\frac{1}{4} \left(9-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2+5 i b n) \cos ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}","\frac{2 x \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2} \, _2F_1\left(\frac{5}{2},\frac{1}{4} \left(5-\frac{2 i}{b n}\right);\frac{1}{4} \left(9-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2+5 i b n) \cos ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}",1,"(2*x*(1 + E^((2*I)*a)*(c*x^n)^((2*I)*b))^(5/2)*Hypergeometric2F1[5/2, (5 - (2*I)/(b*n))/4, (9 - (2*I)/(b*n))/4, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((2 + (5*I)*b*n)*Cos[a + b*Log[c*x^n]]^(5/2))","A",3,3,15,0.2000,1,"{4484, 4492, 364}"
121,1,63,0,0.0435381,"\int \frac{1}{x \cos ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[1/(x*Cos[a + b*Log[c*x^n]]^(5/2)),x]","\frac{2 F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{3 b n}+\frac{2 \sin \left(a+b \log \left(c x^n\right)\right)}{3 b n \cos ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}","\frac{2 F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{3 b n}+\frac{2 \sin \left(a+b \log \left(c x^n\right)\right)}{3 b n \cos ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}",1,"(2*EllipticF[(a + b*Log[c*x^n])/2, 2])/(3*b*n) + (2*Sin[a + b*Log[c*x^n]])/(3*b*n*Cos[a + b*Log[c*x^n]]^(3/2))","A",3,2,19,0.1053,1,"{2636, 2641}"
122,1,48,0,0.0361138,"\int \frac{1}{\cos ^{\frac{3}{2}}(a-2 i \log (c x))} \, dx","Int[Cos[a - (2*I)*Log[c*x]]^(-3/2),x]","-\frac{e^{-2 i a} \left(1+e^{2 i a} c^4 x^4\right)}{2 c^4 x^3 \cos ^{\frac{3}{2}}(a-2 i \log (c x))}","-\frac{e^{-2 i a} \left(1+e^{2 i a} c^4 x^4\right)}{2 c^4 x^3 \cos ^{\frac{3}{2}}(a-2 i \log (c x))}",1,"-(1 + c^4*E^((2*I)*a)*x^4)/(2*c^4*E^((2*I)*a)*x^3*Cos[a - (2*I)*Log[c*x]]^(3/2))","A",3,3,15,0.2000,1,"{4484, 4482, 261}"
123,1,260,0,0.1247689,"\int x^m \cos ^4\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^m*Cos[a + b*Log[c*x^n]]^4,x]","\frac{(m+1) x^{m+1} \cos ^4\left(a+b \log \left(c x^n\right)\right)}{16 b^2 n^2+(m+1)^2}+\frac{12 b^2 (m+1) n^2 x^{m+1} \cos ^2\left(a+b \log \left(c x^n\right)\right)}{20 b^2 (m+1)^2 n^2+64 b^4 n^4+(m+1)^4}+\frac{4 b n x^{m+1} \sin \left(a+b \log \left(c x^n\right)\right) \cos ^3\left(a+b \log \left(c x^n\right)\right)}{16 b^2 n^2+(m+1)^2}+\frac{24 b^3 n^3 x^{m+1} \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{20 b^2 (m+1)^2 n^2+64 b^4 n^4+(m+1)^4}+\frac{24 b^4 n^4 x^{m+1}}{(m+1) \left(4 b^2 n^2+(m+1)^2\right) \left(16 b^2 n^2+(m+1)^2\right)}","\frac{(m+1) x^{m+1} \cos ^4\left(a+b \log \left(c x^n\right)\right)}{16 b^2 n^2+(m+1)^2}+\frac{12 b^2 (m+1) n^2 x^{m+1} \cos ^2\left(a+b \log \left(c x^n\right)\right)}{\left(4 b^2 n^2+(m+1)^2\right) \left(16 b^2 n^2+(m+1)^2\right)}+\frac{4 b n x^{m+1} \sin \left(a+b \log \left(c x^n\right)\right) \cos ^3\left(a+b \log \left(c x^n\right)\right)}{16 b^2 n^2+(m+1)^2}+\frac{24 b^3 n^3 x^{m+1} \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{\left(4 b^2 n^2+(m+1)^2\right) \left(16 b^2 n^2+(m+1)^2\right)}+\frac{24 b^4 n^4 x^{m+1}}{(m+1) \left(4 b^2 n^2+(m+1)^2\right) \left(16 b^2 n^2+(m+1)^2\right)}",1,"(24*b^4*n^4*x^(1 + m))/((1 + m)*((1 + m)^2 + 4*b^2*n^2)*((1 + m)^2 + 16*b^2*n^2)) + (12*b^2*(1 + m)*n^2*x^(1 + m)*Cos[a + b*Log[c*x^n]]^2)/((1 + m)^4 + 20*b^2*(1 + m)^2*n^2 + 64*b^4*n^4) + ((1 + m)*x^(1 + m)*Cos[a + b*Log[c*x^n]]^4)/((1 + m)^2 + 16*b^2*n^2) + (24*b^3*n^3*x^(1 + m)*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/((1 + m)^4 + 20*b^2*(1 + m)^2*n^2 + 64*b^4*n^4) + (4*b*n*x^(1 + m)*Cos[a + b*Log[c*x^n]]^3*Sin[a + b*Log[c*x^n]])/((1 + m)^2 + 16*b^2*n^2)","A",3,2,17,0.1176,1,"{4488, 30}"
124,1,201,0,0.0781204,"\int x^m \cos ^3\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^m*Cos[a + b*Log[c*x^n]]^3,x]","\frac{6 b^3 n^3 x^{m+1} \sin \left(a+b \log \left(c x^n\right)\right)}{\left(b^2 n^2+(m+1)^2\right) \left(9 b^2 n^2+(m+1)^2\right)}+\frac{(m+1) x^{m+1} \cos ^3\left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+(m+1)^2}+\frac{6 b^2 (m+1) n^2 x^{m+1} \cos \left(a+b \log \left(c x^n\right)\right)}{\left(b^2 n^2+(m+1)^2\right) \left(9 b^2 n^2+(m+1)^2\right)}+\frac{3 b n x^{m+1} \sin \left(a+b \log \left(c x^n\right)\right) \cos ^2\left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+(m+1)^2}","\frac{6 b^3 n^3 x^{m+1} \sin \left(a+b \log \left(c x^n\right)\right)}{\left(b^2 n^2+(m+1)^2\right) \left(9 b^2 n^2+(m+1)^2\right)}+\frac{(m+1) x^{m+1} \cos ^3\left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+(m+1)^2}+\frac{6 b^2 (m+1) n^2 x^{m+1} \cos \left(a+b \log \left(c x^n\right)\right)}{\left(b^2 n^2+(m+1)^2\right) \left(9 b^2 n^2+(m+1)^2\right)}+\frac{3 b n x^{m+1} \sin \left(a+b \log \left(c x^n\right)\right) \cos ^2\left(a+b \log \left(c x^n\right)\right)}{9 b^2 n^2+(m+1)^2}",1,"(6*b^2*(1 + m)*n^2*x^(1 + m)*Cos[a + b*Log[c*x^n]])/(((1 + m)^2 + b^2*n^2)*((1 + m)^2 + 9*b^2*n^2)) + ((1 + m)*x^(1 + m)*Cos[a + b*Log[c*x^n]]^3)/((1 + m)^2 + 9*b^2*n^2) + (6*b^3*n^3*x^(1 + m)*Sin[a + b*Log[c*x^n]])/(((1 + m)^2 + b^2*n^2)*((1 + m)^2 + 9*b^2*n^2)) + (3*b*n*x^(1 + m)*Cos[a + b*Log[c*x^n]]^2*Sin[a + b*Log[c*x^n]])/((1 + m)^2 + 9*b^2*n^2)","A",2,2,17,0.1176,1,"{4488, 4486}"
125,1,120,0,0.0318313,"\int x^m \cos ^2\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^m*Cos[a + b*Log[c*x^n]]^2,x]","\frac{(m+1) x^{m+1} \cos ^2\left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+(m+1)^2}+\frac{2 b n x^{m+1} \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+(m+1)^2}+\frac{2 b^2 n^2 x^{m+1}}{(m+1) \left(4 b^2 n^2+(m+1)^2\right)}","\frac{(m+1) x^{m+1} \cos ^2\left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+(m+1)^2}+\frac{2 b n x^{m+1} \sin \left(a+b \log \left(c x^n\right)\right) \cos \left(a+b \log \left(c x^n\right)\right)}{4 b^2 n^2+(m+1)^2}+\frac{2 b^2 n^2 x^{m+1}}{(m+1) \left(4 b^2 n^2+(m+1)^2\right)}",1,"(2*b^2*n^2*x^(1 + m))/((1 + m)*((1 + m)^2 + 4*b^2*n^2)) + ((1 + m)*x^(1 + m)*Cos[a + b*Log[c*x^n]]^2)/((1 + m)^2 + 4*b^2*n^2) + (2*b*n*x^(1 + m)*Cos[a + b*Log[c*x^n]]*Sin[a + b*Log[c*x^n]])/((1 + m)^2 + 4*b^2*n^2)","A",2,2,17,0.1176,1,"{4488, 30}"
126,1,70,0,0.0164579,"\int x^m \cos \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^m*Cos[a + b*Log[c*x^n]],x]","\frac{b n x^{m+1} \sin \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+(m+1)^2}+\frac{(m+1) x^{m+1} \cos \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+(m+1)^2}","\frac{b n x^{m+1} \sin \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+(m+1)^2}+\frac{(m+1) x^{m+1} \cos \left(a+b \log \left(c x^n\right)\right)}{b^2 n^2+(m+1)^2}",1,"((1 + m)*x^(1 + m)*Cos[a + b*Log[c*x^n]])/((1 + m)^2 + b^2*n^2) + (b*n*x^(1 + m)*Sin[a + b*Log[c*x^n]])/((1 + m)^2 + b^2*n^2)","A",1,1,15,0.06667,1,"{4486}"
127,1,126,0,0.1009603,"\int x^m \cos ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^m*Cos[a + b*Log[c*x^n]]^(3/2),x]","\frac{2 x^{m+1} \, _2F_1\left(-\frac{3}{2},\frac{1}{4} \left(-\frac{2 i (m+1)}{b n}-3\right);-\frac{2 i m-b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \cos ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{(-3 i b n+2 m+2) \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2}}","\frac{2 x^{m+1} \, _2F_1\left(-\frac{3}{2},-\frac{2 i m+3 b n+2 i}{4 b n};-\frac{2 i m-b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \cos ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{(-3 i b n+2 m+2) \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2}}",1,"(2*x^(1 + m)*Cos[a + b*Log[c*x^n]]^(3/2)*Hypergeometric2F1[-3/2, (-3 - ((2*I)*(1 + m))/(b*n))/4, -(2*I + (2*I)*m - b*n)/(4*b*n), -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((2 + 2*m - (3*I)*b*n)*(1 + E^((2*I)*a)*(c*x^n)^((2*I)*b))^(3/2))","A",3,3,19,0.1579,1,"{4494, 4492, 364}"
128,1,126,0,0.0990102,"\int x^m \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)} \, dx","Int[x^m*Sqrt[Cos[a + b*Log[c*x^n]]],x]","\frac{2 x^{m+1} \, _2F_1\left(-\frac{1}{2},\frac{1}{4} \left(-\frac{2 i (m+1)}{b n}-1\right);-\frac{2 i m-3 b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)}}{(-i b n+2 m+2) \sqrt{1+e^{2 i a} \left(c x^n\right)^{2 i b}}}","\frac{2 x^{m+1} \, _2F_1\left(-\frac{1}{2},-\frac{2 i m+b n+2 i}{4 b n};-\frac{2 i m-3 b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)}}{(-i b n+2 m+2) \sqrt{1+e^{2 i a} \left(c x^n\right)^{2 i b}}}",1,"(2*x^(1 + m)*Sqrt[Cos[a + b*Log[c*x^n]]]*Hypergeometric2F1[-1/2, (-1 - ((2*I)*(1 + m))/(b*n))/4, -(2*I + (2*I)*m - 3*b*n)/(4*b*n), -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((2 + 2*m - I*b*n)*Sqrt[1 + E^((2*I)*a)*(c*x^n)^((2*I)*b)])","A",3,3,19,0.1579,1,"{4494, 4492, 364}"
129,1,130,0,0.0928662,"\int \frac{x^m}{\sqrt{\cos \left(a+b \log \left(c x^n\right)\right)}} \, dx","Int[x^m/Sqrt[Cos[a + b*Log[c*x^n]]],x]","\frac{2 x^{m+1} \sqrt{1+e^{2 i a} \left(c x^n\right)^{2 i b}} \, _2F_1\left(\frac{1}{2},-\frac{2 i m-b n+2 i}{4 b n};-\frac{2 i m-5 b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(i b n+2 m+2) \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)}}","\frac{2 x^{m+1} \sqrt{1+e^{2 i a} \left(c x^n\right)^{2 i b}} \, _2F_1\left(\frac{1}{2},-\frac{2 i m-b n+2 i}{4 b n};-\frac{2 i m-5 b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(i b n+2 m+2) \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)}}",1,"(2*x^(1 + m)*Sqrt[1 + E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Hypergeometric2F1[1/2, -(2*I + (2*I)*m - b*n)/(4*b*n), -(2*I + (2*I)*m - 5*b*n)/(4*b*n), -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((2 + 2*m + I*b*n)*Sqrt[Cos[a + b*Log[c*x^n]]])","A",3,3,19,0.1579,1,"{4494, 4492, 364}"
130,1,126,0,0.0986783,"\int \frac{x^m}{\cos ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[x^m/Cos[a + b*Log[c*x^n]]^(3/2),x]","\frac{2 x^{m+1} \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{1}{4} \left(3-\frac{2 i (m+1)}{b n}\right);-\frac{2 i m-7 b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(3 i b n+2 m+2) \cos ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}","\frac{2 x^{m+1} \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \, _2F_1\left(\frac{3}{2},-\frac{2 i m-3 b n+2 i}{4 b n};-\frac{2 i m-7 b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(3 i b n+2 m+2) \cos ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}",1,"(2*x^(1 + m)*(1 + E^((2*I)*a)*(c*x^n)^((2*I)*b))^(3/2)*Hypergeometric2F1[3/2, (3 - ((2*I)*(1 + m))/(b*n))/4, -(2*I + (2*I)*m - 7*b*n)/(4*b*n), -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((2 + 2*m + (3*I)*b*n)*Cos[a + b*Log[c*x^n]]^(3/2))","A",3,3,19,0.1579,1,"{4494, 4492, 364}"
131,1,126,0,0.0996792,"\int \frac{x^m}{\cos ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[x^m/Cos[a + b*Log[c*x^n]]^(5/2),x]","\frac{2 x^{m+1} \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2} \, _2F_1\left(\frac{5}{2},\frac{1}{4} \left(5-\frac{2 i (m+1)}{b n}\right);-\frac{2 i m-9 b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(5 i b n+2 m+2) \cos ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}","\frac{2 x^{m+1} \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2} \, _2F_1\left(\frac{5}{2},-\frac{2 i m-5 b n+2 i}{4 b n};-\frac{2 i m-9 b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(5 i b n+2 m+2) \cos ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}",1,"(2*x^(1 + m)*(1 + E^((2*I)*a)*(c*x^n)^((2*I)*b))^(5/2)*Hypergeometric2F1[5/2, (5 - ((2*I)*(1 + m))/(b*n))/4, -(2*I + (2*I)*m - 9*b*n)/(4*b*n), -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((2 + 2*m + (5*I)*b*n)*Cos[a + b*Log[c*x^n]]^(5/2))","A",3,3,19,0.1579,1,"{4494, 4492, 364}"
132,1,144,0,0.1037917,"\int (e x)^m \cos ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Cos[d*(a + b*Log[c*x^n])]^p,x]","\frac{(e x)^{m+1} \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^{-p} \, _2F_1\left(-p,-\frac{i m+b d n p+i}{2 b d n};\frac{1}{2} \left(-\frac{i (m+1)}{b d n}-p+2\right);-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right) \cos ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e (-i b d n p+m+1)}","\frac{(e x)^{m+1} \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^{-p} \, _2F_1\left(-p,-\frac{i m+b d n p+i}{2 b d n};\frac{1}{2} \left(-\frac{i (m+1)}{b d n}-p+2\right);-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right) \cos ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e (-i b d n p+m+1)}",1,"((e*x)^(1 + m)*Cos[d*(a + b*Log[c*x^n])]^p*Hypergeometric2F1[-p, -(I + I*m + b*d*n*p)/(2*b*d*n), (2 - (I*(1 + m))/(b*d*n) - p)/2, -(E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d))])/(e*(1 + m - I*b*d*n*p)*(1 + E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d))^p)","A",3,3,21,0.1429,1,"{4494, 4492, 364}"
133,1,114,0,0.0768798,"\int x \cos ^p\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Cos[a + b*Log[c*x^n]]^p,x]","\frac{x^2 \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{-p} \, _2F_1\left(\frac{1}{2} \left(-p-\frac{2 i}{b n}\right),-p;\frac{1}{2} \left(-p-\frac{2 i}{b n}+2\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \cos ^p\left(a+b \log \left(c x^n\right)\right)}{2-i b n p}","\frac{x^2 \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{-p} \, _2F_1\left(\frac{1}{2} \left(-p-\frac{2 i}{b n}\right),-p;\frac{1}{2} \left(-p-\frac{2 i}{b n}+2\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \cos ^p\left(a+b \log \left(c x^n\right)\right)}{2-i b n p}",1,"(x^2*Cos[a + b*Log[c*x^n]]^p*Hypergeometric2F1[((-2*I)/(b*n) - p)/2, -p, (2 - (2*I)/(b*n) - p)/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((2 - I*b*n*p)*(1 + E^((2*I)*a)*(c*x^n)^((2*I)*b))^p)","A",3,3,15,0.2000,1,"{4494, 4492, 364}"
134,1,112,0,0.0706092,"\int \cos ^p\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Cos[a + b*Log[c*x^n]]^p,x]","\frac{x \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{-p} \, _2F_1\left(-p,-\frac{b n p+i}{2 b n};\frac{1}{2} \left(-p-\frac{i}{b n}+2\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \cos ^p\left(a+b \log \left(c x^n\right)\right)}{1-i b n p}","\frac{x \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{-p} \, _2F_1\left(-p,-\frac{b n p+i}{2 b n};\frac{1}{2} \left(-p-\frac{i}{b n}+2\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \cos ^p\left(a+b \log \left(c x^n\right)\right)}{1-i b n p}",1,"(x*Cos[a + b*Log[c*x^n]]^p*Hypergeometric2F1[-p, -(I + b*n*p)/(2*b*n), (2 - I/(b*n) - p)/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((1 - I*b*n*p)*(1 + E^((2*I)*a)*(c*x^n)^((2*I)*b))^p)","A",3,3,13,0.2308,1,"{4484, 4492, 364}"
135,0,0,0,0.0300232,"\int x^3 \tan (a+i \log (x)) \, dx","Int[x^3*Tan[a + I*Log[x]],x]","\int x^3 \tan (a+i \log (x)) \, dx","-i e^{2 i a} x^2+i e^{4 i a} \log \left(x^2+e^{2 i a}\right)+\frac{i x^4}{4}",1,"Defer[Int][x^3*Tan[a + I*Log[x]], x]","F",0,0,0,0,-1,"{}"
136,0,0,0,0.022892,"\int x^2 \tan (a+i \log (x)) \, dx","Int[x^2*Tan[a + I*Log[x]],x]","\int x^2 \tan (a+i \log (x)) \, dx","-2 i e^{2 i a} x+2 i e^{3 i a} \tan ^{-1}\left(e^{-i a} x\right)+\frac{i x^3}{3}",1,"Defer[Int][x^2*Tan[a + I*Log[x]], x]","F",0,0,0,0,-1,"{}"
137,0,0,0,0.017491,"\int x \tan (a+i \log (x)) \, dx","Int[x*Tan[a + I*Log[x]],x]","\int x \tan (a+i \log (x)) \, dx","\frac{i x^2}{2}-i e^{2 i a} \log \left(x^2+e^{2 i a}\right)",1,"Defer[Int][x*Tan[a + I*Log[x]], x]","F",0,0,0,0,-1,"{}"
138,0,0,0,0.0074411,"\int \tan (a+i \log (x)) \, dx","Int[Tan[a + I*Log[x]],x]","\int \tan (a+i \log (x)) \, dx","i x-2 i e^{i a} \tan ^{-1}\left(e^{-i a} x\right)",1,"Defer[Int][Tan[a + I*Log[x]], x]","F",0,0,0,0,-1,"{}"
139,1,14,0,0.0127726,"\int \frac{\tan (a+i \log (x))}{x} \, dx","Int[Tan[a + I*Log[x]]/x,x]","i \log (\cos (a+i \log (x)))","i \log (\cos (a+i \log (x)))",1,"I*Log[Cos[a + I*Log[x]]]","A",2,1,13,0.07692,1,"{3475}"
140,0,0,0,0.0277522,"\int \frac{\tan (a+i \log (x))}{x^2} \, dx","Int[Tan[a + I*Log[x]]/x^2,x]","\int \frac{\tan (a+i \log (x))}{x^2} \, dx","2 i e^{-i a} \tan ^{-1}\left(e^{-i a} x\right)+\frac{i}{x}",1,"Defer[Int][Tan[a + I*Log[x]]/x^2, x]","F",0,0,0,0,-1,"{}"
141,0,0,0,0.0267757,"\int \frac{\tan (a+i \log (x))}{x^3} \, dx","Int[Tan[a + I*Log[x]]/x^3,x]","\int \frac{\tan (a+i \log (x))}{x^3} \, dx","\frac{i}{2 x^2}-i e^{-2 i a} \log \left(1+\frac{e^{2 i a}}{x^2}\right)",1,"Defer[Int][Tan[a + I*Log[x]]/x^3, x]","F",0,0,0,0,-1,"{}"
142,0,0,0,0.0270119,"\int \frac{\tan (a+i \log (x))}{x^4} \, dx","Int[Tan[a + I*Log[x]]/x^4,x]","\int \frac{\tan (a+i \log (x))}{x^4} \, dx","-\frac{2 i e^{-2 i a}}{x}-2 i e^{-3 i a} \tan ^{-1}\left(e^{-i a} x\right)+\frac{i}{3 x^3}",1,"Defer[Int][Tan[a + I*Log[x]]/x^4, x]","F",0,0,0,0,-1,"{}"
143,0,0,0,0.0699981,"\int x^3 \tan ^2(a+i \log (x)) \, dx","Int[x^3*Tan[a + I*Log[x]]^2,x]","\int x^3 \tan ^2(a+i \log (x)) \, dx","2 e^{2 i a} x^2-\frac{2 e^{6 i a}}{x^2+e^{2 i a}}-4 e^{4 i a} \log \left(x^2+e^{2 i a}\right)-\frac{x^4}{4}",1,"Defer[Int][x^3*Tan[a + I*Log[x]]^2, x]","F",0,0,0,0,-1,"{}"
144,0,0,0,0.0498105,"\int x^2 \tan ^2(a+i \log (x)) \, dx","Int[x^2*Tan[a + I*Log[x]]^2,x]","\int x^2 \tan ^2(a+i \log (x)) \, dx","-\frac{2 e^{2 i a} x^3}{x^2+e^{2 i a}}+6 e^{2 i a} x-6 e^{3 i a} \tan ^{-1}\left(e^{-i a} x\right)-\frac{x^3}{3}",1,"Defer[Int][x^2*Tan[a + I*Log[x]]^2, x]","F",0,0,0,0,-1,"{}"
145,0,0,0,0.0318918,"\int x \tan ^2(a+i \log (x)) \, dx","Int[x*Tan[a + I*Log[x]]^2,x]","\int x \tan ^2(a+i \log (x)) \, dx","\frac{2 e^{4 i a}}{x^2+e^{2 i a}}+2 e^{2 i a} \log \left(x^2+e^{2 i a}\right)-\frac{x^2}{2}",1,"Defer[Int][x*Tan[a + I*Log[x]]^2, x]","F",0,0,0,0,-1,"{}"
146,0,0,0,0.0104115,"\int \tan ^2(a+i \log (x)) \, dx","Int[Tan[a + I*Log[x]]^2,x]","\int \tan ^2(a+i \log (x)) \, dx","-\frac{2 e^{2 i a} x}{x^2+e^{2 i a}}+2 e^{i a} \tan ^{-1}\left(e^{-i a} x\right)-x",1,"Defer[Int][Tan[a + I*Log[x]]^2, x]","F",0,0,0,0,-1,"{}"
147,1,18,0,0.0249887,"\int \frac{\tan ^2(a+i \log (x))}{x} \, dx","Int[Tan[a + I*Log[x]]^2/x,x]","-\log (x)-i \tan (a+i \log (x))","-\log (x)-i \tan (a+i \log (x))",1,"-Log[x] - I*Tan[a + I*Log[x]]","A",3,2,15,0.1333,1,"{3473, 8}"
148,0,0,0,0.0491912,"\int \frac{\tan ^2(a+i \log (x))}{x^2} \, dx","Int[Tan[a + I*Log[x]]^2/x^2,x]","\int \frac{\tan ^2(a+i \log (x))}{x^2} \, dx","\frac{3 x}{x^2+e^{2 i a}}+\frac{e^{2 i a}}{x \left(x^2+e^{2 i a}\right)}+2 e^{-i a} \tan ^{-1}\left(e^{-i a} x\right)",1,"Defer[Int][Tan[a + I*Log[x]]^2/x^2, x]","F",0,0,0,0,-1,"{}"
149,0,0,0,0.052695,"\int \frac{\tan ^2(a+i \log (x))}{x^3} \, dx","Int[Tan[a + I*Log[x]]^2/x^3,x]","\int \frac{\tan ^2(a+i \log (x))}{x^3} \, dx","-\frac{2 e^{-2 i a}}{1+\frac{e^{2 i a}}{x^2}}-2 e^{-2 i a} \log \left(1+\frac{e^{2 i a}}{x^2}\right)+\frac{1}{2 x^2}",1,"Defer[Int][Tan[a + I*Log[x]]^2/x^3, x]","F",0,0,0,0,-1,"{}"
150,0,0,0,0.0436427,"\int (e x)^m \tan (a+i \log (x)) \, dx","Int[(e*x)^m*Tan[a + I*Log[x]],x]","\int (e x)^m \tan (a+i \log (x)) \, dx","\frac{2 i (e x)^{m+1} \, _2F_1\left(1,\frac{1}{2} (-m-1);\frac{1-m}{2};-\frac{e^{2 i a}}{x^2}\right)}{e (m+1)}-\frac{i (e x)^{m+1}}{e (m+1)}",1,"Defer[Int][(e*x)^m*Tan[a + I*Log[x]], x]","F",0,0,0,0,-1,"{}"
151,0,0,0,0.0868889,"\int (e x)^m \tan ^2(a+i \log (x)) \, dx","Int[(e*x)^m*Tan[a + I*Log[x]]^2,x]","\int (e x)^m \tan ^2(a+i \log (x)) \, dx","-2 x (e x)^m \, _2F_1\left(1,\frac{1}{2} (-m-1);\frac{1-m}{2};-\frac{e^{2 i a}}{x^2}\right)+\frac{2 x (e x)^m}{1+\frac{e^{2 i a}}{x^2}}-\frac{x (e x)^m}{m+1}",1,"Defer[Int][(e*x)^m*Tan[a + I*Log[x]]^2, x]","F",0,0,0,0,-1,"{}"
152,0,0,0,0.0906369,"\int (e x)^m \tan ^3(a+i \log (x)) \, dx","Int[(e*x)^m*Tan[a + I*Log[x]]^3,x]","\int (e x)^m \tan ^3(a+i \log (x)) \, dx","-\frac{i \left(m^2+2 m+3\right) x (e x)^m \, _2F_1\left(1,\frac{1}{2} (-m-1);\frac{1-m}{2};-\frac{e^{2 i a}}{x^2}\right)}{m+1}+\frac{i e^{-2 i a} x \left(\frac{e^{4 i a} (1-m)}{x^2}+e^{2 i a} (m+3)\right) (e x)^m}{2 \left(1+\frac{e^{2 i a}}{x^2}\right)}+\frac{i x \left(1-\frac{e^{2 i a}}{x^2}\right)^2 (e x)^m}{2 \left(1+\frac{e^{2 i a}}{x^2}\right)^2}-\frac{i (1-m) m x (e x)^m}{2 (m+1)}",1,"Defer[Int][(e*x)^m*Tan[a + I*Log[x]]^3, x]","F",0,0,0,0,-1,"{}"
153,0,0,0,0.0242006,"\int \tan ^p(a+b \log (x)) \, dx","Int[Tan[a + b*Log[x]]^p,x]","\int \tan ^p(a+b \log (x)) \, dx","x \left(1-e^{2 i a} x^{2 i b}\right)^{-p} \left(\frac{i \left(1-e^{2 i a} x^{2 i b}\right)}{1+e^{2 i a} x^{2 i b}}\right)^p \left(1+e^{2 i a} x^{2 i b}\right)^p F_1\left(-\frac{i}{2 b};-p,p;1-\frac{i}{2 b};e^{2 i a} x^{2 i b},-e^{2 i a} x^{2 i b}\right)",1,"Defer[Int][Tan[a + b*Log[x]]^p, x]","F",0,0,0,0,-1,"{}"
154,0,0,0,0.129776,"\int (e x)^m \tan ^p(a+b \log (x)) \, dx","Int[(e*x)^m*Tan[a + b*Log[x]]^p,x]","\int (e x)^m \tan ^p(a+b \log (x)) \, dx","\frac{(e x)^{m+1} \left(1-e^{2 i a} x^{2 i b}\right)^{-p} \left(\frac{i \left(1-e^{2 i a} x^{2 i b}\right)}{1+e^{2 i a} x^{2 i b}}\right)^p \left(1+e^{2 i a} x^{2 i b}\right)^p F_1\left(-\frac{i (m+1)}{2 b};-p,p;1-\frac{i (m+1)}{2 b};e^{2 i a} x^{2 i b},-e^{2 i a} x^{2 i b}\right)}{e (m+1)}",1,"Defer[Int][(e*x)^m*Tan[a + b*Log[x]]^p, x]","F",0,0,0,0,-1,"{}"
155,0,0,0,0.0214072,"\int \tan ^p(a+\log (x)) \, dx","Int[Tan[a + Log[x]]^p,x]","\int \tan ^p(a+\log (x)) \, dx","x \left(1-e^{2 i a} x^{2 i}\right)^{-p} \left(\frac{i \left(1-e^{2 i a} x^{2 i}\right)}{1+e^{2 i a} x^{2 i}}\right)^p \left(1+e^{2 i a} x^{2 i}\right)^p F_1\left(-\frac{i}{2};-p,p;1-\frac{i}{2};e^{2 i a} x^{2 i},-e^{2 i a} x^{2 i}\right)",1,"Defer[Int][Tan[a + Log[x]]^p, x]","F",0,0,0,0,-1,"{}"
156,0,0,0,0.0196184,"\int \tan ^p(a+2 \log (x)) \, dx","Int[Tan[a + 2*Log[x]]^p,x]","\int \tan ^p(a+2 \log (x)) \, dx","x \left(1-e^{2 i a} x^{4 i}\right)^{-p} \left(\frac{i \left(1-e^{2 i a} x^{4 i}\right)}{1+e^{2 i a} x^{4 i}}\right)^p \left(1+e^{2 i a} x^{4 i}\right)^p F_1\left(-\frac{i}{4};-p,p;1-\frac{i}{4};e^{2 i a} x^{4 i},-e^{2 i a} x^{4 i}\right)",1,"Defer[Int][Tan[a + 2*Log[x]]^p, x]","F",0,0,0,0,-1,"{}"
157,0,0,0,0.0207789,"\int \tan ^p(a+3 \log (x)) \, dx","Int[Tan[a + 3*Log[x]]^p,x]","\int \tan ^p(a+3 \log (x)) \, dx","x \left(1-e^{2 i a} x^{6 i}\right)^{-p} \left(\frac{i \left(1-e^{2 i a} x^{6 i}\right)}{1+e^{2 i a} x^{6 i}}\right)^p \left(1+e^{2 i a} x^{6 i}\right)^p F_1\left(-\frac{i}{6};-p,p;1-\frac{i}{6};e^{2 i a} x^{6 i},-e^{2 i a} x^{6 i}\right)",1,"Defer[Int][Tan[a + 3*Log[x]]^p, x]","F",0,0,0,0,-1,"{}"
158,0,0,0,0.0433235,"\int x^3 \tan \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x^3*Tan[d*(a + b*Log[c*x^n])],x]","\int x^3 \tan \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","\frac{1}{2} i x^4 \, _2F_1\left(1,-\frac{2 i}{b d n};1-\frac{2 i}{b d n};-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)-\frac{i x^4}{4}",1,"Defer[Int][x^3*Tan[d*(a + b*Log[c*x^n])], x]","F",0,0,0,0,-1,"{}"
159,0,0,0,0.0312679,"\int x^2 \tan \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x^2*Tan[d*(a + b*Log[c*x^n])],x]","\int x^2 \tan \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","\frac{2}{3} i x^3 \, _2F_1\left(1,-\frac{3 i}{2 b d n};1-\frac{3 i}{2 b d n};-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)-\frac{i x^3}{3}",1,"Defer[Int][x^2*Tan[d*(a + b*Log[c*x^n])], x]","F",0,0,0,0,-1,"{}"
160,0,0,0,0.0248683,"\int x \tan \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x*Tan[d*(a + b*Log[c*x^n])],x]","\int x \tan \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","i x^2 \, _2F_1\left(1,-\frac{i}{b d n};1-\frac{i}{b d n};-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)-\frac{i x^2}{2}",1,"Defer[Int][x*Tan[d*(a + b*Log[c*x^n])], x]","F",0,0,0,0,-1,"{}"
161,0,0,0,0.0117656,"\int \tan \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[Tan[d*(a + b*Log[c*x^n])],x]","\int \tan \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","2 i x \, _2F_1\left(1,-\frac{i}{2 b d n};1-\frac{i}{2 b d n};-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)-i x",1,"Defer[Int][Tan[d*(a + b*Log[c*x^n])], x]","F",0,0,0,0,-1,"{}"
162,1,26,0,0.0181544,"\int \frac{\tan \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x} \, dx","Int[Tan[d*(a + b*Log[c*x^n])]/x,x]","-\frac{\log \left(\cos \left(a d+b d \log \left(c x^n\right)\right)\right)}{b d n}","-\frac{\log \left(\cos \left(a d+b d \log \left(c x^n\right)\right)\right)}{b d n}",1,"-(Log[Cos[a*d + b*d*Log[c*x^n]]]/(b*d*n))","A",2,1,17,0.05882,1,"{3475}"
163,0,0,0,0.0308557,"\int \frac{\tan \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","Int[Tan[d*(a + b*Log[c*x^n])]/x^2,x]","\int \frac{\tan \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","\frac{i}{x}-\frac{2 i \, _2F_1\left(1,\frac{i}{2 b d n};1+\frac{i}{2 b d n};-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{x}",1,"Defer[Int][Tan[d*(a + b*Log[c*x^n])]/x^2, x]","F",0,0,0,0,-1,"{}"
164,0,0,0,0.0305873,"\int \frac{\tan \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","Int[Tan[d*(a + b*Log[c*x^n])]/x^3,x]","\int \frac{\tan \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","\frac{i}{2 x^2}-\frac{i \, _2F_1\left(1,\frac{i}{b d n};1+\frac{i}{b d n};-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{x^2}",1,"Defer[Int][Tan[d*(a + b*Log[c*x^n])]/x^3, x]","F",0,0,0,0,-1,"{}"
165,0,0,0,0.0900549,"\int x^3 \tan ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x^3*Tan[d*(a + b*Log[c*x^n])]^2,x]","\int x^3 \tan ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","-\frac{2 i x^4 \, _2F_1\left(1,-\frac{2 i}{b d n};1-\frac{2 i}{b d n};-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n}+\frac{i x^4 \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}+\frac{x^4 (-b d n+4 i)}{4 b d n}",1,"Defer[Int][x^3*Tan[d*(a + b*Log[c*x^n])]^2, x]","F",0,0,0,0,-1,"{}"
166,0,0,0,0.0688039,"\int x^2 \tan ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x^2*Tan[d*(a + b*Log[c*x^n])]^2,x]","\int x^2 \tan ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","-\frac{2 i x^3 \, _2F_1\left(1,-\frac{3 i}{2 b d n};1-\frac{3 i}{2 b d n};-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n}+\frac{i x^3 \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}+\frac{x^3 (-b d n+3 i)}{3 b d n}",1,"Defer[Int][x^2*Tan[d*(a + b*Log[c*x^n])]^2, x]","F",0,0,0,0,-1,"{}"
167,0,0,0,0.0438573,"\int x \tan ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x*Tan[d*(a + b*Log[c*x^n])]^2,x]","\int x \tan ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","-\frac{2 i x^2 \, _2F_1\left(1,-\frac{i}{b d n};1-\frac{i}{b d n};-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n}+\frac{i x^2 \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}+\frac{x^2 (-b d n+2 i)}{2 b d n}",1,"Defer[Int][x*Tan[d*(a + b*Log[c*x^n])]^2, x]","F",0,0,0,0,-1,"{}"
168,0,0,0,0.0140475,"\int \tan ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[Tan[d*(a + b*Log[c*x^n])]^2,x]","\int \tan ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","-\frac{2 i x \, _2F_1\left(1,-\frac{i}{2 b d n};1-\frac{i}{2 b d n};-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n}+\frac{i x \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}+\frac{x (-b d n+i)}{b d n}",1,"Defer[Int][Tan[d*(a + b*Log[c*x^n])]^2, x]","F",0,0,0,0,-1,"{}"
169,1,29,0,0.0289976,"\int \frac{\tan ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x} \, dx","Int[Tan[d*(a + b*Log[c*x^n])]^2/x,x]","\frac{\tan \left(a d+b d \log \left(c x^n\right)\right)}{b d n}-\log (x)","\frac{\tan \left(a d+b d \log \left(c x^n\right)\right)}{b d n}-\log (x)",1,"-Log[x] + Tan[a*d + b*d*Log[c*x^n]]/(b*d*n)","A",3,2,19,0.1053,1,"{3473, 8}"
170,0,0,0,0.0551413,"\int \frac{\tan ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","Int[Tan[d*(a + b*Log[c*x^n])]^2/x^2,x]","\int \frac{\tan ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","-\frac{2 i \, _2F_1\left(1,\frac{i}{2 b d n};1+\frac{i}{2 b d n};-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n x}+\frac{i \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n x \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}+\frac{1+\frac{i}{b d n}}{x}",1,"Defer[Int][Tan[d*(a + b*Log[c*x^n])]^2/x^2, x]","F",0,0,0,0,-1,"{}"
171,0,0,0,0.053629,"\int \frac{\tan ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","Int[Tan[d*(a + b*Log[c*x^n])]^2/x^3,x]","\int \frac{\tan ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","-\frac{2 i \, _2F_1\left(1,\frac{i}{b d n};1+\frac{i}{b d n};-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n x^2}+\frac{i \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n x^2 \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}+\frac{1+\frac{2 i}{b d n}}{2 x^2}",1,"Defer[Int][Tan[d*(a + b*Log[c*x^n])]^2/x^3, x]","F",0,0,0,0,-1,"{}"
172,1,43,0,0.0342154,"\int \frac{\tan ^3\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Tan[a + b*Log[c*x^n]]^3/x,x]","\frac{\tan ^2\left(a+b \log \left(c x^n\right)\right)}{2 b n}+\frac{\log \left(\cos \left(a+b \log \left(c x^n\right)\right)\right)}{b n}","\frac{\tan ^2\left(a+b \log \left(c x^n\right)\right)}{2 b n}+\frac{\log \left(\cos \left(a+b \log \left(c x^n\right)\right)\right)}{b n}",1,"Log[Cos[a + b*Log[c*x^n]]]/(b*n) + Tan[a + b*Log[c*x^n]]^2/(2*b*n)","A",3,2,17,0.1176,1,"{3473, 3475}"
173,1,45,0,0.0375052,"\int \frac{\tan ^4\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Tan[a + b*Log[c*x^n]]^4/x,x]","\frac{\tan ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}-\frac{\tan \left(a+b \log \left(c x^n\right)\right)}{b n}+\log (x)","\frac{\tan ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}-\frac{\tan \left(a+b \log \left(c x^n\right)\right)}{b n}+\log (x)",1,"Log[x] - Tan[a + b*Log[c*x^n]]/(b*n) + Tan[a + b*Log[c*x^n]]^3/(3*b*n)","A",4,2,17,0.1176,1,"{3473, 8}"
174,1,67,0,0.044337,"\int \frac{\tan ^5\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Tan[a + b*Log[c*x^n]]^5/x,x]","\frac{\tan ^4\left(a+b \log \left(c x^n\right)\right)}{4 b n}-\frac{\tan ^2\left(a+b \log \left(c x^n\right)\right)}{2 b n}-\frac{\log \left(\cos \left(a+b \log \left(c x^n\right)\right)\right)}{b n}","\frac{\tan ^4\left(a+b \log \left(c x^n\right)\right)}{4 b n}-\frac{\tan ^2\left(a+b \log \left(c x^n\right)\right)}{2 b n}-\frac{\log \left(\cos \left(a+b \log \left(c x^n\right)\right)\right)}{b n}",1,"-(Log[Cos[a + b*Log[c*x^n]]]/(b*n)) - Tan[a + b*Log[c*x^n]]^2/(2*b*n) + Tan[a + b*Log[c*x^n]]^4/(4*b*n)","A",4,2,17,0.1176,1,"{3473, 3475}"
175,0,0,0,0.0478934,"\int (e x)^m \tan \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Tan[d*(a + b*Log[c*x^n])],x]","\int (e x)^m \tan \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","\frac{2 i (e x)^{m+1} \, _2F_1\left(1,-\frac{i (m+1)}{2 b d n};1-\frac{i (m+1)}{2 b d n};-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{e (m+1)}-\frac{i (e x)^{m+1}}{e (m+1)}",1,"Defer[Int][(e*x)^m*Tan[d*(a + b*Log[c*x^n])], x]","F",0,0,0,0,-1,"{}"
176,0,0,0,0.0821511,"\int (e x)^m \tan ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Tan[d*(a + b*Log[c*x^n])]^2,x]","\int (e x)^m \tan ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","-\frac{2 i (e x)^{m+1} \, _2F_1\left(1,-\frac{i (m+1)}{2 b d n};1-\frac{i (m+1)}{2 b d n};-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d e n}+\frac{i (e x)^{m+1} \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d e n \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}+\frac{(e x)^{m+1} (-b d n+i (m+1))}{b d e (m+1) n}",1,"Defer[Int][(e*x)^m*Tan[d*(a + b*Log[c*x^n])]^2, x]","F",0,0,0,0,-1,"{}"
177,0,0,0,0.0759238,"\int (e x)^m \tan ^3\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Tan[d*(a + b*Log[c*x^n])]^3,x]","\int (e x)^m \tan ^3\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","\frac{i (e x)^{m+1} \left(-2 b^2 d^2 n^2+m^2+2 m+1\right) \, _2F_1\left(1,-\frac{i (m+1)}{2 b d n};1-\frac{i (m+1)}{2 b d n};-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b^2 d^2 e (m+1) n^2}-\frac{i e^{-2 i a d} (e x)^{m+1} \left(\frac{e^{2 i a d} (-2 i b d n+m+1)}{n}-\frac{e^{4 i a d} (2 i b d n+m+1) \left(c x^n\right)^{2 i b d}}{n}\right)}{2 b^2 d^2 e n \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}-\frac{(e x)^{m+1} \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^2}{2 b d e n \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^2}-\frac{(e x)^{m+1} (-b d n+i (m+1)) (2 i b d n+m+1)}{2 b^2 d^2 e (m+1) n^2}",1,"Defer[Int][(e*x)^m*Tan[d*(a + b*Log[c*x^n])]^3, x]","F",0,0,0,0,-1,"{}"
178,0,0,0,0.0148668,"\int \tan ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[Tan[d*(a + b*Log[c*x^n])]^p,x]","\int \tan ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","x \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^{-p} \left(\frac{i \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{1+e^{2 i a d} \left(c x^n\right)^{2 i b d}}\right)^p \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^p F_1\left(-\frac{i}{2 b d n};-p,p;1-\frac{i}{2 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d},-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)",1,"Defer[Int][Tan[d*(a + b*Log[c*x^n])]^p, x]","F",0,0,0,0,-1,"{}"
179,0,0,0,0.1041725,"\int (e x)^m \tan ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Tan[d*(a + b*Log[c*x^n])]^p,x]","\int (e x)^m \tan ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","\frac{(e x)^{m+1} \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^{-p} \left(\frac{i \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{1+e^{2 i a d} \left(c x^n\right)^{2 i b d}}\right)^p \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^p F_1\left(-\frac{i (m+1)}{2 b d n};-p,p;1-\frac{i (m+1)}{2 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d},-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{e (m+1)}",1,"Defer[Int][(e*x)^m*Tan[d*(a + b*Log[c*x^n])]^p, x]","F",0,0,0,0,-1,"{}"
180,1,201,0,0.1392939,"\int \frac{\tan ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Tan[a + b*Log[c*x^n]]^(5/2)/x,x]","\frac{2 \tan ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{3 b n}+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}-\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}","\frac{2 \tan ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{3 b n}+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}-\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}",1,"ArcTan[1 - Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n) - ArcTan[1 + Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n) - Log[1 - Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]] + Tan[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n) + Log[1 + Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]] + Tan[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n) + (2*Tan[a + b*Log[c*x^n]]^(3/2))/(3*b*n)","A",13,9,19,0.4737,1,"{3473, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
181,1,199,0,0.1277094,"\int \frac{\tan ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Tan[a + b*Log[c*x^n]]^(3/2)/x,x]","\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}+\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{2 \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}}{b n}","\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}+\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{2 \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}}{b n}",1,"ArcTan[1 - Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n) - ArcTan[1 + Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n) + Log[1 - Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]] + Tan[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n) - Log[1 + Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]] + Tan[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n) + (2*Sqrt[Tan[a + b*Log[c*x^n]]])/(b*n)","A",13,9,19,0.4737,1,"{3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
182,1,176,0,0.1204403,"\int \frac{\sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}}{x} \, dx","Int[Sqrt[Tan[a + b*Log[c*x^n]]]/x,x]","-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}+\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}","-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}+\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}",1,"-(ArcTan[1 - Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n)) + ArcTan[1 + Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n) + Log[1 - Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]] + Tan[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n) - Log[1 + Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]] + Tan[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n)","A",12,8,19,0.4211,1,"{3476, 329, 297, 1162, 617, 204, 1165, 628}"
183,1,176,0,0.1205691,"\int \frac{1}{x \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}} \, dx","Int[1/(x*Sqrt[Tan[a + b*Log[c*x^n]]]),x]","-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}-\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}","-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}-\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}",1,"-(ArcTan[1 - Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n)) + ArcTan[1 + Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n) - Log[1 - Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]] + Tan[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n) + Log[1 + Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]] + Tan[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n)","A",12,8,19,0.4211,1,"{3476, 329, 211, 1165, 628, 1162, 617, 204}"
184,1,199,0,0.1336434,"\int \frac{1}{x \tan ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[1/(x*Tan[a + b*Log[c*x^n]]^(3/2)),x]","\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}-\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{2}{b n \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}}","\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}-\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{2}{b n \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}}",1,"ArcTan[1 - Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n) - ArcTan[1 + Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n) - Log[1 - Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]] + Tan[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n) + Log[1 + Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]] + Tan[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n) - 2/(b*n*Sqrt[Tan[a + b*Log[c*x^n]]])","A",13,9,19,0.4737,1,"{3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
185,1,201,0,0.1283436,"\int \frac{1}{x \tan ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[1/(x*Tan[a + b*Log[c*x^n]]^(5/2)),x]","\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}-\frac{2}{3 b n \tan ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}+\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}","\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}-\frac{2}{3 b n \tan ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}+\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{\log \left(\tan \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\tan \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}",1,"ArcTan[1 - Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n) - ArcTan[1 + Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n) + Log[1 - Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]] + Tan[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n) - Log[1 + Sqrt[2]*Sqrt[Tan[a + b*Log[c*x^n]]] + Tan[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n) - 2/(3*b*n*Tan[a + b*Log[c*x^n]]^(3/2))","A",13,9,19,0.4737,1,"{3474, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
186,0,0,0,0.0260149,"\int x^3 \cot (a+i \log (x)) \, dx","Int[x^3*Cot[a + I*Log[x]],x]","\int x^3 \cot (a+i \log (x)) \, dx","-i e^{2 i a} x^2-i e^{4 i a} \log \left(-x^2+e^{2 i a}\right)-\frac{i x^4}{4}",1,"Defer[Int][x^3*Cot[a + I*Log[x]], x]","F",0,0,0,0,-1,"{}"
187,0,0,0,0.0223548,"\int x^2 \cot (a+i \log (x)) \, dx","Int[x^2*Cot[a + I*Log[x]],x]","\int x^2 \cot (a+i \log (x)) \, dx","-2 i e^{2 i a} x+2 i e^{3 i a} \tanh ^{-1}\left(e^{-i a} x\right)-\frac{i x^3}{3}",1,"Defer[Int][x^2*Cot[a + I*Log[x]], x]","F",0,0,0,0,-1,"{}"
188,0,0,0,0.014523,"\int x \cot (a+i \log (x)) \, dx","Int[x*Cot[a + I*Log[x]],x]","\int x \cot (a+i \log (x)) \, dx","-i e^{2 i a} \log \left(-x^2+e^{2 i a}\right)-\frac{i x^2}{2}",1,"Defer[Int][x*Cot[a + I*Log[x]], x]","F",0,0,0,0,-1,"{}"
189,0,0,0,0.0072593,"\int \cot (a+i \log (x)) \, dx","Int[Cot[a + I*Log[x]],x]","\int \cot (a+i \log (x)) \, dx","2 i e^{i a} \tanh ^{-1}\left(e^{-i a} x\right)-i x",1,"Defer[Int][Cot[a + I*Log[x]], x]","F",0,0,0,0,-1,"{}"
190,1,14,0,0.012911,"\int \frac{\cot (a+i \log (x))}{x} \, dx","Int[Cot[a + I*Log[x]]/x,x]","-i \log (\sin (a+i \log (x)))","-i \log (\sin (a+i \log (x)))",1,"(-I)*Log[Sin[a + I*Log[x]]]","A",2,1,13,0.07692,1,"{3475}"
191,0,0,0,0.0246961,"\int \frac{\cot (a+i \log (x))}{x^2} \, dx","Int[Cot[a + I*Log[x]]/x^2,x]","\int \frac{\cot (a+i \log (x))}{x^2} \, dx","2 i e^{-i a} \tanh ^{-1}\left(e^{-i a} x\right)-\frac{i}{x}",1,"Defer[Int][Cot[a + I*Log[x]]/x^2, x]","F",0,0,0,0,-1,"{}"
192,0,0,0,0.0240748,"\int \frac{\cot (a+i \log (x))}{x^3} \, dx","Int[Cot[a + I*Log[x]]/x^3,x]","\int \frac{\cot (a+i \log (x))}{x^3} \, dx","-i e^{-2 i a} \log \left(1-\frac{e^{2 i a}}{x^2}\right)-\frac{i}{2 x^2}",1,"Defer[Int][Cot[a + I*Log[x]]/x^3, x]","F",0,0,0,0,-1,"{}"
193,0,0,0,0.025074,"\int \frac{\cot (a+i \log (x))}{x^4} \, dx","Int[Cot[a + I*Log[x]]/x^4,x]","\int \frac{\cot (a+i \log (x))}{x^4} \, dx","-\frac{2 i e^{-2 i a}}{x}+2 i e^{-3 i a} \tanh ^{-1}\left(e^{-i a} x\right)-\frac{i}{3 x^3}",1,"Defer[Int][Cot[a + I*Log[x]]/x^4, x]","F",0,0,0,0,-1,"{}"
194,0,0,0,0.0650718,"\int x^3 \cot ^2(a+i \log (x)) \, dx","Int[x^3*Cot[a + I*Log[x]]^2,x]","\int x^3 \cot ^2(a+i \log (x)) \, dx","-2 e^{2 i a} x^2-\frac{2 e^{6 i a}}{-x^2+e^{2 i a}}-4 e^{4 i a} \log \left(-x^2+e^{2 i a}\right)-\frac{x^4}{4}",1,"Defer[Int][x^3*Cot[a + I*Log[x]]^2, x]","F",0,0,0,0,-1,"{}"
195,0,0,0,0.0509217,"\int x^2 \cot ^2(a+i \log (x)) \, dx","Int[x^2*Cot[a + I*Log[x]]^2,x]","\int x^2 \cot ^2(a+i \log (x)) \, dx","-\frac{2 e^{2 i a} x^3}{-x^2+e^{2 i a}}-6 e^{2 i a} x+6 e^{3 i a} \tanh ^{-1}\left(e^{-i a} x\right)-\frac{x^3}{3}",1,"Defer[Int][x^2*Cot[a + I*Log[x]]^2, x]","F",0,0,0,0,-1,"{}"
196,0,0,0,0.0356521,"\int x \cot ^2(a+i \log (x)) \, dx","Int[x*Cot[a + I*Log[x]]^2,x]","\int x \cot ^2(a+i \log (x)) \, dx","-\frac{2 e^{4 i a}}{-x^2+e^{2 i a}}-2 e^{2 i a} \log \left(-x^2+e^{2 i a}\right)-\frac{x^2}{2}",1,"Defer[Int][x*Cot[a + I*Log[x]]^2, x]","F",0,0,0,0,-1,"{}"
197,0,0,0,0.0105502,"\int \cot ^2(a+i \log (x)) \, dx","Int[Cot[a + I*Log[x]]^2,x]","\int \cot ^2(a+i \log (x)) \, dx","-\frac{2 e^{2 i a} x}{-x^2+e^{2 i a}}+2 e^{i a} \tanh ^{-1}\left(e^{-i a} x\right)-x",1,"Defer[Int][Cot[a + I*Log[x]]^2, x]","F",0,0,0,0,-1,"{}"
198,1,18,0,0.0235847,"\int \frac{\cot ^2(a+i \log (x))}{x} \, dx","Int[Cot[a + I*Log[x]]^2/x,x]","-\log (x)+i \cot (a+i \log (x))","-\log (x)+i \cot (a+i \log (x))",1,"I*Cot[a + I*Log[x]] - Log[x]","A",3,2,15,0.1333,1,"{3473, 8}"
199,0,0,0,0.0478845,"\int \frac{\cot ^2(a+i \log (x))}{x^2} \, dx","Int[Cot[a + I*Log[x]]^2/x^2,x]","\int \frac{\cot ^2(a+i \log (x))}{x^2} \, dx","-\frac{3 x}{-x^2+e^{2 i a}}+\frac{e^{2 i a}}{x \left(-x^2+e^{2 i a}\right)}-2 e^{-i a} \tanh ^{-1}\left(e^{-i a} x\right)",1,"Defer[Int][Cot[a + I*Log[x]]^2/x^2, x]","F",0,0,0,0,-1,"{}"
200,0,0,0,0.050647,"\int \frac{\cot ^2(a+i \log (x))}{x^3} \, dx","Int[Cot[a + I*Log[x]]^2/x^3,x]","\int \frac{\cot ^2(a+i \log (x))}{x^3} \, dx","\frac{2 e^{-2 i a}}{1-\frac{e^{2 i a}}{x^2}}+2 e^{-2 i a} \log \left(1-\frac{e^{2 i a}}{x^2}\right)+\frac{1}{2 x^2}",1,"Defer[Int][Cot[a + I*Log[x]]^2/x^3, x]","F",0,0,0,0,-1,"{}"
201,0,0,0,0.040328,"\int (e x)^m \cot (a+i \log (x)) \, dx","Int[(e*x)^m*Cot[a + I*Log[x]],x]","\int (e x)^m \cot (a+i \log (x)) \, dx","\frac{i (e x)^{m+1}}{e (m+1)}-\frac{2 i (e x)^{m+1} \, _2F_1\left(1,\frac{1}{2} (-m-1);\frac{1-m}{2};\frac{e^{2 i a}}{x^2}\right)}{e (m+1)}",1,"Defer[Int][(e*x)^m*Cot[a + I*Log[x]], x]","F",0,0,0,0,-1,"{}"
202,0,0,0,0.0695071,"\int (e x)^m \cot ^2(a+i \log (x)) \, dx","Int[(e*x)^m*Cot[a + I*Log[x]]^2,x]","\int (e x)^m \cot ^2(a+i \log (x)) \, dx","-2 x (e x)^m \, _2F_1\left(1,\frac{1}{2} (-m-1);\frac{1-m}{2};\frac{e^{2 i a}}{x^2}\right)+\frac{2 x (e x)^m}{1-\frac{e^{2 i a}}{x^2}}-\frac{x (e x)^m}{m+1}",1,"Defer[Int][(e*x)^m*Cot[a + I*Log[x]]^2, x]","F",0,0,0,0,-1,"{}"
203,0,0,0,0.0772087,"\int (e x)^m \cot ^3(a+i \log (x)) \, dx","Int[(e*x)^m*Cot[a + I*Log[x]]^3,x]","\int (e x)^m \cot ^3(a+i \log (x)) \, dx","\frac{i \left(m^2+2 m+3\right) x (e x)^m \, _2F_1\left(1,\frac{1}{2} (-m-1);\frac{1-m}{2};\frac{e^{2 i a}}{x^2}\right)}{m+1}-\frac{i x \left(1+\frac{e^{2 i a}}{x^2}\right)^2 (e x)^m}{2 \left(1-\frac{e^{2 i a}}{x^2}\right)^2}-\frac{i x \left(-\frac{e^{2 i a} (1-m)}{x^2}+m+3\right) (e x)^m}{2 \left(1-\frac{e^{2 i a}}{x^2}\right)}+\frac{i (1-m) m x (e x)^m}{2 (m+1)}",1,"Defer[Int][(e*x)^m*Cot[a + I*Log[x]]^3, x]","F",0,0,0,0,-1,"{}"
204,0,0,0,0.0215861,"\int \cot ^p(a+b \log (x)) \, dx","Int[Cot[a + b*Log[x]]^p,x]","\int \cot ^p(a+b \log (x)) \, dx","x \left(1-e^{2 i a} x^{2 i b}\right)^p \left(1+e^{2 i a} x^{2 i b}\right)^{-p} \left(-\frac{i \left(1+e^{2 i a} x^{2 i b}\right)}{1-e^{2 i a} x^{2 i b}}\right)^p F_1\left(-\frac{i}{2 b};p,-p;1-\frac{i}{2 b};e^{2 i a} x^{2 i b},-e^{2 i a} x^{2 i b}\right)",1,"Defer[Int][Cot[a + b*Log[x]]^p, x]","F",0,0,0,0,-1,"{}"
205,0,0,0,0.1173385,"\int (e x)^m \cot ^p(a+b \log (x)) \, dx","Int[(e*x)^m*Cot[a + b*Log[x]]^p,x]","\int (e x)^m \cot ^p(a+b \log (x)) \, dx","\frac{(e x)^{m+1} \left(1-e^{2 i a} x^{2 i b}\right)^p \left(1+e^{2 i a} x^{2 i b}\right)^{-p} \left(-\frac{i \left(1+e^{2 i a} x^{2 i b}\right)}{1-e^{2 i a} x^{2 i b}}\right)^p F_1\left(-\frac{i (m+1)}{2 b};p,-p;1-\frac{i (m+1)}{2 b};e^{2 i a} x^{2 i b},-e^{2 i a} x^{2 i b}\right)}{e (m+1)}",1,"Defer[Int][(e*x)^m*Cot[a + b*Log[x]]^p, x]","F",0,0,0,0,-1,"{}"
206,0,0,0,0.0200752,"\int \cot ^p(a+\log (x)) \, dx","Int[Cot[a + Log[x]]^p,x]","\int \cot ^p(a+\log (x)) \, dx","x \left(1-e^{2 i a} x^{2 i}\right)^p \left(1+e^{2 i a} x^{2 i}\right)^{-p} \left(-\frac{i \left(1+e^{2 i a} x^{2 i}\right)}{1-e^{2 i a} x^{2 i}}\right)^p F_1\left(-\frac{i}{2};p,-p;1-\frac{i}{2};e^{2 i a} x^{2 i},-e^{2 i a} x^{2 i}\right)",1,"Defer[Int][Cot[a + Log[x]]^p, x]","F",0,0,0,0,-1,"{}"
207,0,0,0,0.0202924,"\int \cot ^p(a+2 \log (x)) \, dx","Int[Cot[a + 2*Log[x]]^p,x]","\int \cot ^p(a+2 \log (x)) \, dx","x \left(1-e^{2 i a} x^{4 i}\right)^p \left(1+e^{2 i a} x^{4 i}\right)^{-p} \left(-\frac{i \left(1+e^{2 i a} x^{4 i}\right)}{1-e^{2 i a} x^{4 i}}\right)^p F_1\left(-\frac{i}{4};p,-p;1-\frac{i}{4};e^{2 i a} x^{4 i},-e^{2 i a} x^{4 i}\right)",1,"Defer[Int][Cot[a + 2*Log[x]]^p, x]","F",0,0,0,0,-1,"{}"
208,0,0,0,0.0210843,"\int \cot ^p(a+3 \log (x)) \, dx","Int[Cot[a + 3*Log[x]]^p,x]","\int \cot ^p(a+3 \log (x)) \, dx","x \left(1-e^{2 i a} x^{6 i}\right)^p \left(1+e^{2 i a} x^{6 i}\right)^{-p} \left(-\frac{i \left(1+e^{2 i a} x^{6 i}\right)}{1-e^{2 i a} x^{6 i}}\right)^p F_1\left(-\frac{i}{6};p,-p;1-\frac{i}{6};e^{2 i a} x^{6 i},-e^{2 i a} x^{6 i}\right)",1,"Defer[Int][Cot[a + 3*Log[x]]^p, x]","F",0,0,0,0,-1,"{}"
209,0,0,0,0.0352325,"\int x^3 \cot \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x^3*Cot[d*(a + b*Log[c*x^n])],x]","\int x^3 \cot \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","\frac{i x^4}{4}-\frac{1}{2} i x^4 \, _2F_1\left(1,-\frac{2 i}{b d n};1-\frac{2 i}{b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)",1,"Defer[Int][x^3*Cot[d*(a + b*Log[c*x^n])], x]","F",0,0,0,0,-1,"{}"
210,0,0,0,0.0290022,"\int x^2 \cot \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x^2*Cot[d*(a + b*Log[c*x^n])],x]","\int x^2 \cot \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","\frac{i x^3}{3}-\frac{2}{3} i x^3 \, _2F_1\left(1,-\frac{3 i}{2 b d n};1-\frac{3 i}{2 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)",1,"Defer[Int][x^2*Cot[d*(a + b*Log[c*x^n])], x]","F",0,0,0,0,-1,"{}"
211,0,0,0,0.0225825,"\int x \cot \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x*Cot[d*(a + b*Log[c*x^n])],x]","\int x \cot \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","\frac{i x^2}{2}-i x^2 \, _2F_1\left(1,-\frac{i}{b d n};1-\frac{i}{b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)",1,"Defer[Int][x*Cot[d*(a + b*Log[c*x^n])], x]","F",0,0,0,0,-1,"{}"
212,0,0,0,0.01151,"\int \cot \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[Cot[d*(a + b*Log[c*x^n])],x]","\int \cot \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","i x-2 i x \, _2F_1\left(1,-\frac{i}{2 b d n};1-\frac{i}{2 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)",1,"Defer[Int][Cot[d*(a + b*Log[c*x^n])], x]","F",0,0,0,0,-1,"{}"
213,1,25,0,0.0184988,"\int \frac{\cot \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x} \, dx","Int[Cot[d*(a + b*Log[c*x^n])]/x,x]","\frac{\log \left(\sin \left(a d+b d \log \left(c x^n\right)\right)\right)}{b d n}","\frac{\log \left(\sin \left(a d+b d \log \left(c x^n\right)\right)\right)}{b d n}",1,"Log[Sin[a*d + b*d*Log[c*x^n]]]/(b*d*n)","A",2,1,17,0.05882,1,"{3475}"
214,0,0,0,0.0295843,"\int \frac{\cot \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","Int[Cot[d*(a + b*Log[c*x^n])]/x^2,x]","\int \frac{\cot \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","\frac{2 i \, _2F_1\left(1,\frac{i}{2 b d n};1+\frac{i}{2 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{x}-\frac{i}{x}",1,"Defer[Int][Cot[d*(a + b*Log[c*x^n])]/x^2, x]","F",0,0,0,0,-1,"{}"
215,0,0,0,0.029018,"\int \frac{\cot \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","Int[Cot[d*(a + b*Log[c*x^n])]/x^3,x]","\int \frac{\cot \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","\frac{i \, _2F_1\left(1,\frac{i}{b d n};1+\frac{i}{b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{x^2}-\frac{i}{2 x^2}",1,"Defer[Int][Cot[d*(a + b*Log[c*x^n])]/x^3, x]","F",0,0,0,0,-1,"{}"
216,0,0,0,0.0853566,"\int x^3 \cot ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x^3*Cot[d*(a + b*Log[c*x^n])]^2,x]","\int x^3 \cot ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","-\frac{2 i x^4 \, _2F_1\left(1,-\frac{2 i}{b d n};1-\frac{2 i}{b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n}+\frac{i x^4 \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}+\frac{x^4 (-b d n+4 i)}{4 b d n}",1,"Defer[Int][x^3*Cot[d*(a + b*Log[c*x^n])]^2, x]","F",0,0,0,0,-1,"{}"
217,0,0,0,0.0611011,"\int x^2 \cot ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x^2*Cot[d*(a + b*Log[c*x^n])]^2,x]","\int x^2 \cot ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","-\frac{2 i x^3 \, _2F_1\left(1,-\frac{3 i}{2 b d n};1-\frac{3 i}{2 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n}+\frac{i x^3 \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}+\frac{x^3 (-b d n+3 i)}{3 b d n}",1,"Defer[Int][x^2*Cot[d*(a + b*Log[c*x^n])]^2, x]","F",0,0,0,0,-1,"{}"
218,0,0,0,0.0439753,"\int x \cot ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x*Cot[d*(a + b*Log[c*x^n])]^2,x]","\int x \cot ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","-\frac{2 i x^2 \, _2F_1\left(1,-\frac{i}{b d n};1-\frac{i}{b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n}+\frac{i x^2 \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}+\frac{x^2 (-b d n+2 i)}{2 b d n}",1,"Defer[Int][x*Cot[d*(a + b*Log[c*x^n])]^2, x]","F",0,0,0,0,-1,"{}"
219,0,0,0,0.0139643,"\int \cot ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[Cot[d*(a + b*Log[c*x^n])]^2,x]","\int \cot ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","-\frac{2 i x \, _2F_1\left(1,-\frac{i}{2 b d n};1-\frac{i}{2 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n}+\frac{i x \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}+\frac{x (-b d n+i)}{b d n}",1,"Defer[Int][Cot[d*(a + b*Log[c*x^n])]^2, x]","F",0,0,0,0,-1,"{}"
220,1,30,0,0.0300002,"\int \frac{\cot ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x} \, dx","Int[Cot[d*(a + b*Log[c*x^n])]^2/x,x]","-\frac{\cot \left(a d+b d \log \left(c x^n\right)\right)}{b d n}-\log (x)","-\frac{\cot \left(a d+b d \log \left(c x^n\right)\right)}{b d n}-\log (x)",1,"-(Cot[a*d + b*d*Log[c*x^n]]/(b*d*n)) - Log[x]","A",3,2,19,0.1053,1,"{3473, 8}"
221,0,0,0,0.0569329,"\int \frac{\cot ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","Int[Cot[d*(a + b*Log[c*x^n])]^2/x^2,x]","\int \frac{\cot ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","-\frac{2 i \, _2F_1\left(1,\frac{i}{2 b d n};1+\frac{i}{2 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n x}+\frac{i \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n x \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}+\frac{1+\frac{i}{b d n}}{x}",1,"Defer[Int][Cot[d*(a + b*Log[c*x^n])]^2/x^2, x]","F",0,0,0,0,-1,"{}"
222,0,0,0,0.0533164,"\int \frac{\cot ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","Int[Cot[d*(a + b*Log[c*x^n])]^2/x^3,x]","\int \frac{\cot ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","-\frac{2 i \, _2F_1\left(1,\frac{i}{b d n};1+\frac{i}{b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n x^2}+\frac{i \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d n x^2 \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}+\frac{1+\frac{2 i}{b d n}}{2 x^2}",1,"Defer[Int][Cot[d*(a + b*Log[c*x^n])]^2/x^3, x]","F",0,0,0,0,-1,"{}"
223,1,44,0,0.0365938,"\int \frac{\cot ^3\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Cot[a + b*Log[c*x^n]]^3/x,x]","-\frac{\log \left(\sin \left(a+b \log \left(c x^n\right)\right)\right)}{b n}-\frac{\cot ^2\left(a+b \log \left(c x^n\right)\right)}{2 b n}","-\frac{\log \left(\sin \left(a+b \log \left(c x^n\right)\right)\right)}{b n}-\frac{\cot ^2\left(a+b \log \left(c x^n\right)\right)}{2 b n}",1,"-Cot[a + b*Log[c*x^n]]^2/(2*b*n) - Log[Sin[a + b*Log[c*x^n]]]/(b*n)","A",3,2,17,0.1176,1,"{3473, 3475}"
224,1,44,0,0.038864,"\int \frac{\cot ^4\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Cot[a + b*Log[c*x^n]]^4/x,x]","-\frac{\cot ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}+\frac{\cot \left(a+b \log \left(c x^n\right)\right)}{b n}+\log (x)","-\frac{\cot ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}+\frac{\cot \left(a+b \log \left(c x^n\right)\right)}{b n}+\log (x)",1,"Cot[a + b*Log[c*x^n]]/(b*n) - Cot[a + b*Log[c*x^n]]^3/(3*b*n) + Log[x]","A",4,2,17,0.1176,1,"{3473, 8}"
225,1,66,0,0.0455594,"\int \frac{\cot ^5\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Cot[a + b*Log[c*x^n]]^5/x,x]","\frac{\log \left(\sin \left(a+b \log \left(c x^n\right)\right)\right)}{b n}-\frac{\cot ^4\left(a+b \log \left(c x^n\right)\right)}{4 b n}+\frac{\cot ^2\left(a+b \log \left(c x^n\right)\right)}{2 b n}","\frac{\log \left(\sin \left(a+b \log \left(c x^n\right)\right)\right)}{b n}-\frac{\cot ^4\left(a+b \log \left(c x^n\right)\right)}{4 b n}+\frac{\cot ^2\left(a+b \log \left(c x^n\right)\right)}{2 b n}",1,"Cot[a + b*Log[c*x^n]]^2/(2*b*n) - Cot[a + b*Log[c*x^n]]^4/(4*b*n) + Log[Sin[a + b*Log[c*x^n]]]/(b*n)","A",4,2,17,0.1176,1,"{3473, 3475}"
226,0,0,0,0.0477099,"\int (e x)^m \cot \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Cot[d*(a + b*Log[c*x^n])],x]","\int (e x)^m \cot \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","\frac{i (e x)^{m+1}}{e (m+1)}-\frac{2 i (e x)^{m+1} \, _2F_1\left(1,-\frac{i (m+1)}{2 b d n};1-\frac{i (m+1)}{2 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{e (m+1)}",1,"Defer[Int][(e*x)^m*Cot[d*(a + b*Log[c*x^n])], x]","F",0,0,0,0,-1,"{}"
227,0,0,0,0.0784244,"\int (e x)^m \cot ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Cot[d*(a + b*Log[c*x^n])]^2,x]","\int (e x)^m \cot ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","-\frac{2 i (e x)^{m+1} \, _2F_1\left(1,-\frac{i (m+1)}{2 b d n};1-\frac{i (m+1)}{2 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d e n}+\frac{i (e x)^{m+1} \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b d e n \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}+\frac{(e x)^{m+1} (-b d n+i (m+1))}{b d e (m+1) n}",1,"Defer[Int][(e*x)^m*Cot[d*(a + b*Log[c*x^n])]^2, x]","F",0,0,0,0,-1,"{}"
228,0,0,0,0.0726727,"\int (e x)^m \cot ^3\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Cot[d*(a + b*Log[c*x^n])]^3,x]","\int (e x)^m \cot ^3\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","-\frac{i (e x)^{m+1} \left(-2 b^2 d^2 n^2+m^2+2 m+1\right) \, _2F_1\left(1,-\frac{i (m+1)}{2 b d n};1-\frac{i (m+1)}{2 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{b^2 d^2 e (m+1) n^2}+\frac{i e^{-2 i a d} (e x)^{m+1} \left(\frac{e^{4 i a d} (2 i b d n+m+1) \left(c x^n\right)^{2 i b d}}{n}+\frac{e^{2 i a d} (-2 i b d n+m+1)}{n}\right)}{2 b^2 d^2 e n \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}+\frac{(e x)^{m+1} \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^2}{2 b d e n \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^2}+\frac{(e x)^{m+1} (-b d n+i (m+1)) (2 i b d n+m+1)}{2 b^2 d^2 e (m+1) n^2}",1,"Defer[Int][(e*x)^m*Cot[d*(a + b*Log[c*x^n])]^3, x]","F",0,0,0,0,-1,"{}"
229,0,0,0,0.0150207,"\int \cot ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[Cot[d*(a + b*Log[c*x^n])]^p,x]","\int \cot ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","x \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^p \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^{-p} \left(-\frac{i \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{1-e^{2 i a d} \left(c x^n\right)^{2 i b d}}\right)^p F_1\left(-\frac{i}{2 b d n};p,-p;1-\frac{i}{2 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d},-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)",1,"Defer[Int][Cot[d*(a + b*Log[c*x^n])]^p, x]","F",0,0,0,0,-1,"{}"
230,0,0,0,0.1039895,"\int (e x)^m \cot ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Cot[d*(a + b*Log[c*x^n])]^p,x]","\int (e x)^m \cot ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","\frac{(e x)^{m+1} \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^p \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^{-p} \left(-\frac{i \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{1-e^{2 i a d} \left(c x^n\right)^{2 i b d}}\right)^p F_1\left(-\frac{i (m+1)}{2 b d n};p,-p;1-\frac{i (m+1)}{2 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d},-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{e (m+1)}",1,"Defer[Int][(e*x)^m*Cot[d*(a + b*Log[c*x^n])]^p, x]","F",0,0,0,0,-1,"{}"
231,1,201,0,0.1391184,"\int \frac{\cot ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Cot[a + b*Log[c*x^n]]^(5/2)/x,x]","-\frac{2 \cot ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{3 b n}+\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}","-\frac{2 \cot ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{3 b n}+\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}",1,"-(ArcTan[1 - Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n)) + ArcTan[1 + Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n) - (2*Cot[a + b*Log[c*x^n]]^(3/2))/(3*b*n) + Log[1 - Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]] + Cot[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n) - Log[1 + Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]] + Cot[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n)","A",13,9,19,0.4737,1,"{3473, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
232,1,199,0,0.1313852,"\int \frac{\cot ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Cot[a + b*Log[c*x^n]]^(3/2)/x,x]","-\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{2 \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}}{b n}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}","-\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{2 \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}}{b n}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}",1,"-(ArcTan[1 - Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n)) + ArcTan[1 + Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n) - (2*Sqrt[Cot[a + b*Log[c*x^n]]])/(b*n) - Log[1 - Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]] + Cot[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n) + Log[1 + Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]] + Cot[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n)","A",13,9,19,0.4737,1,"{3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
233,1,176,0,0.120996,"\int \frac{\sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}}{x} \, dx","Int[Sqrt[Cot[a + b*Log[c*x^n]]]/x,x]","-\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}","-\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}",1,"ArcTan[1 - Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n) - ArcTan[1 + Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n) - Log[1 - Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]] + Cot[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n) + Log[1 + Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]] + Cot[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n)","A",12,8,19,0.4211,1,"{3476, 329, 297, 1162, 617, 204, 1165, 628}"
234,1,176,0,0.1277021,"\int \frac{1}{x \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}} \, dx","Int[1/(x*Sqrt[Cot[a + b*Log[c*x^n]]]),x]","\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}","\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}",1,"ArcTan[1 - Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n) - ArcTan[1 + Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n) + Log[1 - Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]] + Cot[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n) - Log[1 + Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]] + Cot[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n)","A",12,8,19,0.4211,1,"{3476, 329, 211, 1165, 628, 1162, 617, 204}"
235,1,199,0,0.1315158,"\int \frac{1}{x \cot ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[1/(x*Cot[a + b*Log[c*x^n]]^(3/2)),x]","\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{2}{b n \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}","\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{2}{b n \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}",1,"-(ArcTan[1 - Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n)) + ArcTan[1 + Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n) + 2/(b*n*Sqrt[Cot[a + b*Log[c*x^n]]]) + Log[1 - Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]] + Cot[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n) - Log[1 + Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]] + Cot[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n)","A",13,9,19,0.4737,1,"{3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
236,1,201,0,0.134183,"\int \frac{1}{x \cot ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[1/(x*Cot[a + b*Log[c*x^n]]^(5/2)),x]","\frac{2}{3 b n \cot ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}-\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}","\frac{2}{3 b n \cot ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}-\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}+\frac{\log \left(\cot \left(a+b \log \left(c x^n\right)\right)+\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{2 \sqrt{2} b n}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}\right)}{\sqrt{2} b n}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\cot \left(a+b \log \left(c x^n\right)\right)}+1\right)}{\sqrt{2} b n}",1,"-(ArcTan[1 - Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n)) + ArcTan[1 + Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]]]/(Sqrt[2]*b*n) + 2/(3*b*n*Cot[a + b*Log[c*x^n]]^(3/2)) - Log[1 - Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]] + Cot[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n) + Log[1 + Sqrt[2]*Sqrt[Cot[a + b*Log[c*x^n]]] + Cot[a + b*Log[c*x^n]]]/(2*Sqrt[2]*b*n)","A",13,9,19,0.4737,1,"{3474, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
237,1,87,0,0.0594096,"\int x^2 \sec \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*Sec[a + b*Log[c*x^n]],x]","\frac{2 e^{i a} x^3 \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1-\frac{3 i}{b n}\right);\frac{3}{2} \left(1-\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{3+i b n}","\frac{2 e^{i a} x^3 \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1-\frac{3 i}{b n}\right);\frac{3}{2} \left(1-\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{3+i b n}",1,"(2*E^(I*a)*x^3*(c*x^n)^(I*b)*Hypergeometric2F1[1, (1 - (3*I)/(b*n))/2, (3*(1 - I/(b*n)))/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/(3 + I*b*n)","A",3,3,15,0.2000,1,"{4509, 4505, 364}"
238,1,87,0,0.0517846,"\int x \sec \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Sec[a + b*Log[c*x^n]],x]","\frac{2 e^{i a} x^2 \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1-\frac{2 i}{b n}\right);\frac{1}{2} \left(3-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{2+i b n}","\frac{2 e^{i a} x^2 \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1-\frac{2 i}{b n}\right);\frac{1}{2} \left(3-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{2+i b n}",1,"(2*E^(I*a)*x^2*(c*x^n)^(I*b)*Hypergeometric2F1[1, (1 - (2*I)/(b*n))/2, (3 - (2*I)/(b*n))/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/(2 + I*b*n)","A",3,3,13,0.2308,1,"{4509, 4505, 364}"
239,1,85,0,0.0500636,"\int \sec \left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sec[a + b*Log[c*x^n]],x]","\frac{2 e^{i a} x \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1-\frac{i}{b n}\right);\frac{1}{2} \left(3-\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{1+i b n}","\frac{2 e^{i a} x \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1-\frac{i}{b n}\right);\frac{1}{2} \left(3-\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{1+i b n}",1,"(2*E^(I*a)*x*(c*x^n)^(I*b)*Hypergeometric2F1[1, (1 - I/(b*n))/2, (3 - I/(b*n))/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/(1 + I*b*n)","A",3,3,11,0.2727,1,"{4503, 4505, 364}"
240,1,19,0,0.0163493,"\int \frac{\sec \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Sec[a + b*Log[c*x^n]]/x,x]","\frac{\tanh ^{-1}\left(\sin \left(a+b \log \left(c x^n\right)\right)\right)}{b n}","\frac{\tanh ^{-1}\left(\sin \left(a+b \log \left(c x^n\right)\right)\right)}{b n}",1,"ArcTanh[Sin[a + b*Log[c*x^n]]]/(b*n)","A",2,1,15,0.06667,1,"{3770}"
241,1,87,0,0.0609986,"\int \frac{\sec \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[Sec[a + b*Log[c*x^n]]/x^2,x]","-\frac{2 e^{i a} \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1+\frac{i}{b n}\right);\frac{1}{2} \left(3+\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x (1-i b n)}","-\frac{2 e^{i a} \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1+\frac{i}{b n}\right);\frac{1}{2} \left(3+\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x (1-i b n)}",1,"(-2*E^(I*a)*(c*x^n)^(I*b)*Hypergeometric2F1[1, (1 + I/(b*n))/2, (3 + I/(b*n))/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((1 - I*b*n)*x)","A",3,3,15,0.2000,1,"{4509, 4505, 364}"
242,1,87,0,0.0564884,"\int \frac{\sec \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[Sec[a + b*Log[c*x^n]]/x^3,x]","-\frac{2 e^{i a} \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1+\frac{2 i}{b n}\right);\frac{1}{2} \left(3+\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x^2 (2-i b n)}","-\frac{2 e^{i a} \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1+\frac{2 i}{b n}\right);\frac{1}{2} \left(3+\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x^2 (2-i b n)}",1,"(-2*E^(I*a)*(c*x^n)^(I*b)*Hypergeometric2F1[1, (1 + (2*I)/(b*n))/2, (3 + (2*I)/(b*n))/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((2 - I*b*n)*x^2)","A",3,3,15,0.2000,1,"{4509, 4505, 364}"
243,1,87,0,0.075054,"\int x^2 \sec ^2\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*Sec[a + b*Log[c*x^n]]^2,x]","\frac{4 e^{2 i a} x^3 \left(c x^n\right)^{2 i b} \, _2F_1\left(2,\frac{1}{2} \left(2-\frac{3 i}{b n}\right);\frac{1}{2} \left(4-\frac{3 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{3+2 i b n}","\frac{4 e^{2 i a} x^3 \left(c x^n\right)^{2 i b} \, _2F_1\left(2,\frac{1}{2} \left(2-\frac{3 i}{b n}\right);\frac{1}{2} \left(4-\frac{3 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{3+2 i b n}",1,"(4*E^((2*I)*a)*x^3*(c*x^n)^((2*I)*b)*Hypergeometric2F1[2, (2 - (3*I)/(b*n))/2, (4 - (3*I)/(b*n))/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/(3 + (2*I)*b*n)","A",3,3,17,0.1765,1,"{4509, 4505, 364}"
244,1,79,0,0.0655583,"\int x \sec ^2\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Sec[a + b*Log[c*x^n]]^2,x]","\frac{2 e^{2 i a} x^2 \left(c x^n\right)^{2 i b} \, _2F_1\left(2,1-\frac{i}{b n};2-\frac{i}{b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{1+i b n}","\frac{2 e^{2 i a} x^2 \left(c x^n\right)^{2 i b} \, _2F_1\left(2,1-\frac{i}{b n};2-\frac{i}{b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{1+i b n}",1,"(2*E^((2*I)*a)*x^2*(c*x^n)^((2*I)*b)*Hypergeometric2F1[2, 1 - I/(b*n), 2 - I/(b*n), -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/(1 + I*b*n)","A",3,3,15,0.2000,1,"{4509, 4505, 364}"
245,1,85,0,0.0625784,"\int \sec ^2\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sec[a + b*Log[c*x^n]]^2,x]","\frac{4 e^{2 i a} x \left(c x^n\right)^{2 i b} \, _2F_1\left(2,\frac{1}{2} \left(2-\frac{i}{b n}\right);\frac{1}{2} \left(4-\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{1+2 i b n}","\frac{4 e^{2 i a} x \left(c x^n\right)^{2 i b} \, _2F_1\left(2,\frac{1}{2} \left(2-\frac{i}{b n}\right);\frac{1}{2} \left(4-\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{1+2 i b n}",1,"(4*E^((2*I)*a)*x*(c*x^n)^((2*I)*b)*Hypergeometric2F1[2, (2 - I/(b*n))/2, (4 - I/(b*n))/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/(1 + (2*I)*b*n)","A",3,3,13,0.2308,1,"{4503, 4505, 364}"
246,1,18,0,0.027744,"\int \frac{\sec ^2\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Sec[a + b*Log[c*x^n]]^2/x,x]","\frac{\tan \left(a+b \log \left(c x^n\right)\right)}{b n}","\frac{\tan \left(a+b \log \left(c x^n\right)\right)}{b n}",1,"Tan[a + b*Log[c*x^n]]/(b*n)","A",3,2,17,0.1176,1,"{3767, 8}"
247,1,87,0,0.0764024,"\int \frac{\sec ^2\left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[Sec[a + b*Log[c*x^n]]^2/x^2,x]","-\frac{4 e^{2 i a} \left(c x^n\right)^{2 i b} \, _2F_1\left(2,\frac{1}{2} \left(2+\frac{i}{b n}\right);\frac{1}{2} \left(4+\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x (1-2 i b n)}","-\frac{4 e^{2 i a} \left(c x^n\right)^{2 i b} \, _2F_1\left(2,\frac{1}{2} \left(2+\frac{i}{b n}\right);\frac{1}{2} \left(4+\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x (1-2 i b n)}",1,"(-4*E^((2*I)*a)*(c*x^n)^((2*I)*b)*Hypergeometric2F1[2, (2 + I/(b*n))/2, (4 + I/(b*n))/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((1 - (2*I)*b*n)*x)","A",3,3,17,0.1765,1,"{4509, 4505, 364}"
248,1,79,0,0.0706627,"\int \frac{\sec ^2\left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[Sec[a + b*Log[c*x^n]]^2/x^3,x]","-\frac{2 e^{2 i a} \left(c x^n\right)^{2 i b} \, _2F_1\left(2,1+\frac{i}{b n};2+\frac{i}{b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x^2 (1-i b n)}","-\frac{2 e^{2 i a} \left(c x^n\right)^{2 i b} \, _2F_1\left(2,1+\frac{i}{b n};2+\frac{i}{b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x^2 (1-i b n)}",1,"(-2*E^((2*I)*a)*(c*x^n)^((2*I)*b)*Hypergeometric2F1[2, 1 + I/(b*n), 2 + I/(b*n), -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((1 - I*b*n)*x^2)","A",3,3,17,0.1765,1,"{4509, 4505, 364}"
249,1,87,0,0.0661174,"\int x \sec ^3\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Sec[a + b*Log[c*x^n]]^3,x]","\frac{8 e^{3 i a} x^2 \left(c x^n\right)^{3 i b} \, _2F_1\left(3,\frac{1}{2} \left(3-\frac{2 i}{b n}\right);\frac{1}{2} \left(5-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{2+3 i b n}","\frac{8 e^{3 i a} x^2 \left(c x^n\right)^{3 i b} \, _2F_1\left(3,\frac{1}{2} \left(3-\frac{2 i}{b n}\right);\frac{1}{2} \left(5-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{2+3 i b n}",1,"(8*E^((3*I)*a)*x^2*(c*x^n)^((3*I)*b)*Hypergeometric2F1[3, (3 - (2*I)/(b*n))/2, (5 - (2*I)/(b*n))/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/(2 + (3*I)*b*n)","A",3,3,15,0.2000,1,"{4509, 4505, 364}"
250,1,85,0,0.0630798,"\int \sec ^3\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sec[a + b*Log[c*x^n]]^3,x]","\frac{8 e^{3 i a} x \left(c x^n\right)^{3 i b} \, _2F_1\left(3,\frac{1}{2} \left(3-\frac{i}{b n}\right);\frac{1}{2} \left(5-\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{1+3 i b n}","\frac{8 e^{3 i a} x \left(c x^n\right)^{3 i b} \, _2F_1\left(3,\frac{1}{2} \left(3-\frac{i}{b n}\right);\frac{1}{2} \left(5-\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{1+3 i b n}",1,"(8*E^((3*I)*a)*x*(c*x^n)^((3*I)*b)*Hypergeometric2F1[3, (3 - I/(b*n))/2, (5 - I/(b*n))/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/(1 + (3*I)*b*n)","A",3,3,13,0.2308,1,"{4503, 4505, 364}"
251,1,55,0,0.0384104,"\int \frac{\sec ^3\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Sec[a + b*Log[c*x^n]]^3/x,x]","\frac{\tanh ^{-1}\left(\sin \left(a+b \log \left(c x^n\right)\right)\right)}{2 b n}+\frac{\tan \left(a+b \log \left(c x^n\right)\right) \sec \left(a+b \log \left(c x^n\right)\right)}{2 b n}","\frac{\tanh ^{-1}\left(\sin \left(a+b \log \left(c x^n\right)\right)\right)}{2 b n}+\frac{\tan \left(a+b \log \left(c x^n\right)\right) \sec \left(a+b \log \left(c x^n\right)\right)}{2 b n}",1,"ArcTanh[Sin[a + b*Log[c*x^n]]]/(2*b*n) + (Sec[a + b*Log[c*x^n]]*Tan[a + b*Log[c*x^n]])/(2*b*n)","A",3,2,17,0.1176,1,"{3768, 3770}"
252,1,87,0,0.0745732,"\int \frac{\sec ^3\left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[Sec[a + b*Log[c*x^n]]^3/x^2,x]","-\frac{8 e^{3 i a} \left(c x^n\right)^{3 i b} \, _2F_1\left(3,\frac{1}{2} \left(3+\frac{i}{b n}\right);\frac{1}{2} \left(5+\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x (1-3 i b n)}","-\frac{8 e^{3 i a} \left(c x^n\right)^{3 i b} \, _2F_1\left(3,\frac{1}{2} \left(3+\frac{i}{b n}\right);\frac{1}{2} \left(5+\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x (1-3 i b n)}",1,"(-8*E^((3*I)*a)*(c*x^n)^((3*I)*b)*Hypergeometric2F1[3, (3 + I/(b*n))/2, (5 + I/(b*n))/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((1 - (3*I)*b*n)*x)","A",3,3,17,0.1765,1,"{4509, 4505, 364}"
253,1,87,0,0.0730395,"\int \frac{\sec ^3\left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[Sec[a + b*Log[c*x^n]]^3/x^3,x]","-\frac{8 e^{3 i a} \left(c x^n\right)^{3 i b} \, _2F_1\left(3,\frac{1}{2} \left(3+\frac{2 i}{b n}\right);\frac{1}{2} \left(5+\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x^2 (2-3 i b n)}","-\frac{8 e^{3 i a} \left(c x^n\right)^{3 i b} \, _2F_1\left(3,\frac{1}{2} \left(3+\frac{2 i}{b n}\right);\frac{1}{2} \left(5+\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x^2 (2-3 i b n)}",1,"(-8*E^((3*I)*a)*(c*x^n)^((3*I)*b)*Hypergeometric2F1[3, (3 + (2*I)/(b*n))/2, (5 + (2*I)/(b*n))/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((2 - (3*I)*b*n)*x^2)","A",3,3,17,0.1765,1,"{4509, 4505, 364}"
254,1,79,0,0.0693265,"\int x \sec ^4\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Sec[a + b*Log[c*x^n]]^4,x]","\frac{8 e^{4 i a} x^2 \left(c x^n\right)^{4 i b} \, _2F_1\left(4,2-\frac{i}{b n};3-\frac{i}{b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{1+2 i b n}","\frac{8 e^{4 i a} x^2 \left(c x^n\right)^{4 i b} \, _2F_1\left(4,2-\frac{i}{b n};3-\frac{i}{b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{1+2 i b n}",1,"(8*E^((4*I)*a)*x^2*(c*x^n)^((4*I)*b)*Hypergeometric2F1[4, 2 - I/(b*n), 3 - I/(b*n), -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/(1 + (2*I)*b*n)","A",3,3,15,0.2000,1,"{4509, 4505, 364}"
255,1,85,0,0.0625623,"\int \sec ^4\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sec[a + b*Log[c*x^n]]^4,x]","\frac{16 e^{4 i a} x \left(c x^n\right)^{4 i b} \, _2F_1\left(4,\frac{1}{2} \left(4-\frac{i}{b n}\right);\frac{1}{2} \left(6-\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{1+4 i b n}","\frac{16 e^{4 i a} x \left(c x^n\right)^{4 i b} \, _2F_1\left(4,\frac{1}{2} \left(4-\frac{i}{b n}\right);\frac{1}{2} \left(6-\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{1+4 i b n}",1,"(16*E^((4*I)*a)*x*(c*x^n)^((4*I)*b)*Hypergeometric2F1[4, (4 - I/(b*n))/2, (6 - I/(b*n))/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/(1 + (4*I)*b*n)","A",3,3,13,0.2308,1,"{4503, 4505, 364}"
256,1,42,0,0.034284,"\int \frac{\sec ^4\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Sec[a + b*Log[c*x^n]]^4/x,x]","\frac{\tan ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}+\frac{\tan \left(a+b \log \left(c x^n\right)\right)}{b n}","\frac{\tan ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}+\frac{\tan \left(a+b \log \left(c x^n\right)\right)}{b n}",1,"Tan[a + b*Log[c*x^n]]/(b*n) + Tan[a + b*Log[c*x^n]]^3/(3*b*n)","A",3,1,17,0.05882,1,"{3767}"
257,1,87,0,0.0753623,"\int \frac{\sec ^4\left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[Sec[a + b*Log[c*x^n]]^4/x^2,x]","-\frac{16 e^{4 i a} \left(c x^n\right)^{4 i b} \, _2F_1\left(4,\frac{1}{2} \left(4+\frac{i}{b n}\right);\frac{1}{2} \left(6+\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x (1-4 i b n)}","-\frac{16 e^{4 i a} \left(c x^n\right)^{4 i b} \, _2F_1\left(4,\frac{1}{2} \left(4+\frac{i}{b n}\right);\frac{1}{2} \left(6+\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x (1-4 i b n)}",1,"(-16*E^((4*I)*a)*(c*x^n)^((4*I)*b)*Hypergeometric2F1[4, (4 + I/(b*n))/2, (6 + I/(b*n))/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((1 - (4*I)*b*n)*x)","A",3,3,17,0.1765,1,"{4509, 4505, 364}"
258,1,79,0,0.0723831,"\int \frac{\sec ^4\left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[Sec[a + b*Log[c*x^n]]^4/x^3,x]","-\frac{8 e^{4 i a} \left(c x^n\right)^{4 i b} \, _2F_1\left(4,2+\frac{i}{b n};3+\frac{i}{b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x^2 (1-2 i b n)}","-\frac{8 e^{4 i a} \left(c x^n\right)^{4 i b} \, _2F_1\left(4,2+\frac{i}{b n};3+\frac{i}{b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x^2 (1-2 i b n)}",1,"(-8*E^((4*I)*a)*(c*x^n)^((4*I)*b)*Hypergeometric2F1[4, 2 + I/(b*n), 3 + I/(b*n), -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((1 - (2*I)*b*n)*x^2)","A",3,3,17,0.1765,1,"{4509, 4505, 364}"
259,1,175,0,0.1328962,"\int \left(-\left(1+b^2 n^2\right) \sec \left(a+b \log \left(c x^n\right)\right)+2 b^2 n^2 \sec ^3\left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[-((1 + b^2*n^2)*Sec[a + b*Log[c*x^n]]) + 2*b^2*n^2*Sec[a + b*Log[c*x^n]]^3,x]","\frac{16 e^{3 i a} b^2 n^2 x \left(c x^n\right)^{3 i b} \, _2F_1\left(3,\frac{1}{2} \left(3-\frac{i}{b n}\right);\frac{1}{2} \left(5-\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{1+3 i b n}-2 e^{i a} x (1-i b n) \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1-\frac{i}{b n}\right);\frac{1}{2} \left(3-\frac{i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)","b n x \tan \left(a+b \log \left(c x^n\right)\right) \sec \left(a+b \log \left(c x^n\right)\right)-x \sec \left(a+b \log \left(c x^n\right)\right)",1,"-2*E^(I*a)*(1 - I*b*n)*x*(c*x^n)^(I*b)*Hypergeometric2F1[1, (1 - I/(b*n))/2, (3 - I/(b*n))/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))] + (16*b^2*E^((3*I)*a)*n^2*x*(c*x^n)^((3*I)*b)*Hypergeometric2F1[3, (3 - I/(b*n))/2, (5 - I/(b*n))/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/(1 + (3*I)*b*n)","C",7,3,44,0.06818,0,"{4503, 4505, 364}"
260,1,146,0,0.2174777,"\int x^m \sec ^3\left(a+2 \log \left(c x^{\frac{1}{2} \sqrt{-(1+m)^2}}\right)\right) \, dx","Int[x^m*Sec[a + 2*Log[c*x^(Sqrt[-(1 + m)^2]/2)]]^3,x]","\frac{8 e^{3 i a} x^{m+1} \left(c x^{\frac{1}{2} \sqrt{-(m+1)^2}}\right)^{6 i} \, _2F_1\left(3,\frac{1}{2} \left(3-\frac{i (m+1)}{\sqrt{-(m+1)^2}}\right);\frac{1}{2} \left(5-\frac{i (m+1)}{\sqrt{-(m+1)^2}}\right);-e^{2 i a} \left(c x^{\frac{1}{2} \sqrt{-(m+1)^2}}\right)^{4 i}\right)}{1-i \left(-3 \sqrt{-(m+1)^2}+i m\right)}","\frac{x^{m+1} \sec \left(a+2 \log \left(c x^{\frac{1}{2} \sqrt{-(m+1)^2}}\right)\right)}{2 (m+1)}+\frac{x^{m+1} \tan \left(a+2 \log \left(c x^{\frac{1}{2} \sqrt{-(m+1)^2}}\right)\right) \sec \left(a+2 \log \left(c x^{\frac{1}{2} \sqrt{-(m+1)^2}}\right)\right)}{2 \sqrt{-(m+1)^2}}",1,"(8*E^((3*I)*a)*x^(1 + m)*(c*x^(Sqrt[-(1 + m)^2]/2))^(6*I)*Hypergeometric2F1[3, (3 - (I*(1 + m))/Sqrt[-(1 + m)^2])/2, (5 - (I*(1 + m))/Sqrt[-(1 + m)^2])/2, -(E^((2*I)*a)*(c*x^(Sqrt[-(1 + m)^2]/2))^(4*I))])/(1 - I*(I*m - 3*Sqrt[-(1 + m)^2]))","C",3,3,31,0.09677,0,"{4509, 4505, 364}"
261,1,45,0,0.0427162,"\int x \sec ^3\left(a+2 \log \left(c x^i\right)\right) \, dx","Int[x*Sec[a + 2*Log[c*x^I]]^3,x]","\frac{e^{i a} x^2 \left(c x^i\right)^{2 i}}{\left(1+e^{2 i a} \left(c x^i\right)^{4 i}\right)^2}","\frac{e^{i a} x^2 \left(c x^i\right)^{2 i}}{\left(1+e^{2 i a} \left(c x^i\right)^{4 i}\right)^2}",1,"(E^(I*a)*(c*x^I)^(2*I)*x^2)/(1 + E^((2*I)*a)*(c*x^I)^(4*I))^2","A",3,3,17,0.1765,1,"{4509, 4505, 261}"
262,1,48,0,0.0349121,"\int \sec ^3\left(a+2 \log \left(c x^{\frac{i}{2}}\right)\right) \, dx","Int[Sec[a + 2*Log[c*x^(I/2)]]^3,x]","\frac{2 e^{i a} x \left(c x^{\frac{i}{2}}\right)^{2 i}}{\left(1+e^{2 i a} \left(c x^{\frac{i}{2}}\right)^{4 i}\right)^2}","\frac{1}{2} x \sec \left(a+2 \log \left(c x^{\frac{i}{2}}\right)\right)-\frac{1}{2} i x \tan \left(a+2 \log \left(c x^{\frac{i}{2}}\right)\right) \sec \left(a+2 \log \left(c x^{\frac{i}{2}}\right)\right)",1,"(2*E^(I*a)*(c*x^(I/2))^(2*I)*x)/(1 + E^((2*I)*a)*(c*x^(I/2))^(4*I))^2","A",3,3,17,0.1765,0,"{4503, 4505, 261}"
263,1,48,0,0.0406423,"\int \sec ^3\left(a+2 \log \left(c x^{-\frac{i}{2}}\right)\right) \, dx","Int[Sec[a + 2*Log[c/x^(I/2)]]^3,x]","\frac{2 e^{3 i a} x \left(c x^{-\frac{i}{2}}\right)^{6 i}}{\left(1+e^{2 i a} \left(c x^{-\frac{i}{2}}\right)^{4 i}\right)^2}","\frac{2 e^{3 i a} x \left(c x^{-\frac{i}{2}}\right)^{6 i}}{\left(1+e^{2 i a} \left(c x^{-\frac{i}{2}}\right)^{4 i}\right)^2}",1,"(2*E^((3*I)*a)*(c/x^(I/2))^(6*I)*x)/(1 + E^((2*I)*a)*(c/x^(I/2))^(4*I))^2","A",3,3,17,0.1765,1,"{4503, 4505, 264}"
264,1,95,0,0.0910376,"\int \sec ^p\left(a+\frac{i \log \left(c x^n\right)}{n (-2+p)}\right) \, dx","Int[Sec[a + (I*Log[c*x^n])/(n*(-2 + p))]^p,x]","\frac{e^{-2 i a} (2-p) x \left(c x^n\right)^{-\frac{2}{n (2-p)}} \left(1+e^{2 i a} \left(c x^n\right)^{\frac{2}{n (2-p)}}\right) \sec ^p\left(a-\frac{i \log \left(c x^n\right)}{n (2-p)}\right)}{2 (1-p)}","\frac{e^{-2 i a} (2-p) x \left(c x^n\right)^{-\frac{2}{n (2-p)}} \left(1+e^{2 i a} \left(c x^n\right)^{\frac{2}{n (2-p)}}\right) \sec ^p\left(a-\frac{i \log \left(c x^n\right)}{n (2-p)}\right)}{2 (1-p)}",1,"((2 - p)*x*(1 + E^((2*I)*a)*(c*x^n)^(2/(n*(2 - p))))*Sec[a - (I*Log[c*x^n])/(n*(2 - p))]^p)/(2*E^((2*I)*a)*(1 - p)*(c*x^n)^(2/(n*(2 - p))))","A",3,3,23,0.1304,1,"{4503, 4507, 261}"
265,1,70,0,0.0751668,"\int \sec ^p\left(a-\frac{i \log \left(c x^n\right)}{n (-2+p)}\right) \, dx","Int[Sec[a - (I*Log[c*x^n])/(n*(-2 + p))]^p,x]","\frac{(2-p) x \left(1+e^{2 i a} \left(c x^n\right)^{-\frac{2}{n (2-p)}}\right) \sec ^p\left(a+\frac{i \log \left(c x^n\right)}{n (2-p)}\right)}{2 (1-p)}","\frac{(2-p) x \left(1+e^{2 i a} \left(c x^n\right)^{-\frac{2}{n (2-p)}}\right) \sec ^p\left(a+\frac{i \log \left(c x^n\right)}{n (2-p)}\right)}{2 (1-p)}",1,"((2 - p)*x*(1 + E^((2*I)*a)/(c*x^n)^(2/(n*(2 - p))))*Sec[a + (I*Log[c*x^n])/(n*(2 - p))]^p)/(2*(1 - p))","A",3,3,23,0.1304,1,"{4503, 4507, 264}"
266,1,109,0,0.0704075,"\int \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)} \, dx","Int[Sqrt[Sec[a + b*Log[c*x^n]]],x]","\frac{2 x \sqrt{1+e^{2 i a} \left(c x^n\right)^{2 i b}} \, _2F_1\left(\frac{1}{2},\frac{1}{4} \left(1-\frac{2 i}{b n}\right);\frac{1}{4} \left(5-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)}}{2+i b n}","\frac{2 x \sqrt{1+e^{2 i a} \left(c x^n\right)^{2 i b}} \, _2F_1\left(\frac{1}{2},\frac{1}{4} \left(1-\frac{2 i}{b n}\right);\frac{1}{4} \left(5-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)}}{2+i b n}",1,"(2*x*Sqrt[1 + E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Hypergeometric2F1[1/2, (1 - (2*I)/(b*n))/4, (5 - (2*I)/(b*n))/4, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))]*Sqrt[Sec[a + b*Log[c*x^n]]])/(2 + I*b*n)","A",3,3,15,0.2000,1,"{4503, 4507, 364}"
267,1,54,0,0.0431732,"\int \frac{\sqrt{\sec \left(a+b \log \left(c x^n\right)\right)}}{x} \, dx","Int[Sqrt[Sec[a + b*Log[c*x^n]]]/x,x]","\frac{2 \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)} \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}","\frac{2 \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)} \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}",1,"(2*Sqrt[Cos[a + b*Log[c*x^n]]]*EllipticF[(a + b*Log[c*x^n])/2, 2]*Sqrt[Sec[a + b*Log[c*x^n]]])/(b*n)","A",3,2,19,0.1053,1,"{3771, 2641}"
268,1,109,0,0.0724252,"\int \sec ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sec[a + b*Log[c*x^n]]^(3/2),x]","\frac{2 x \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{1}{4} \left(3-\frac{2 i}{b n}\right);\frac{1}{4} \left(7-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sec ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{2+3 i b n}","\frac{2 x \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{1}{4} \left(3-\frac{2 i}{b n}\right);\frac{1}{4} \left(7-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sec ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{2+3 i b n}",1,"(2*x*(1 + E^((2*I)*a)*(c*x^n)^((2*I)*b))^(3/2)*Hypergeometric2F1[3/2, (3 - (2*I)/(b*n))/4, (7 - (2*I)/(b*n))/4, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))]*Sec[a + b*Log[c*x^n]]^(3/2))/(2 + (3*I)*b*n)","A",3,3,15,0.2000,1,"{4503, 4507, 364}"
269,1,89,0,0.0609058,"\int \frac{\sec ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Sec[a + b*Log[c*x^n]]^(3/2)/x,x]","\frac{2 \sin \left(a+b \log \left(c x^n\right)\right) \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)}}{b n}-\frac{2 \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)} \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}","\frac{2 \sin \left(a+b \log \left(c x^n\right)\right) \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)}}{b n}-\frac{2 \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)} \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}",1,"(-2*Sqrt[Cos[a + b*Log[c*x^n]]]*EllipticE[(a + b*Log[c*x^n])/2, 2]*Sqrt[Sec[a + b*Log[c*x^n]]])/(b*n) + (2*Sqrt[Sec[a + b*Log[c*x^n]]]*Sin[a + b*Log[c*x^n]])/(b*n)","A",4,3,19,0.1579,1,"{3768, 3771, 2639}"
270,1,109,0,0.0722975,"\int \sec ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sec[a + b*Log[c*x^n]]^(5/2),x]","\frac{2 x \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2} \, _2F_1\left(\frac{5}{2},\frac{1}{4} \left(5-\frac{2 i}{b n}\right);\frac{1}{4} \left(9-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sec ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{2+5 i b n}","\frac{2 x \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2} \, _2F_1\left(\frac{5}{2},\frac{1}{4} \left(5-\frac{2 i}{b n}\right);\frac{1}{4} \left(9-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sec ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{2+5 i b n}",1,"(2*x*(1 + E^((2*I)*a)*(c*x^n)^((2*I)*b))^(5/2)*Hypergeometric2F1[5/2, (5 - (2*I)/(b*n))/4, (9 - (2*I)/(b*n))/4, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))]*Sec[a + b*Log[c*x^n]]^(5/2))/(2 + (5*I)*b*n)","A",3,3,15,0.2000,1,"{4503, 4507, 364}"
271,1,93,0,0.0610006,"\int \frac{\sec ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Sec[a + b*Log[c*x^n]]^(5/2)/x,x]","\frac{2 \sin \left(a+b \log \left(c x^n\right)\right) \sec ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{3 b n}+\frac{2 \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)} \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{3 b n}","\frac{2 \sin \left(a+b \log \left(c x^n\right)\right) \sec ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{3 b n}+\frac{2 \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)} \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{3 b n}",1,"(2*Sqrt[Cos[a + b*Log[c*x^n]]]*EllipticF[(a + b*Log[c*x^n])/2, 2]*Sqrt[Sec[a + b*Log[c*x^n]]])/(3*b*n) + (2*Sec[a + b*Log[c*x^n]]^(3/2)*Sin[a + b*Log[c*x^n]])/(3*b*n)","A",4,3,19,0.1579,1,"{3768, 3771, 2641}"
272,1,110,0,0.0693818,"\int \frac{1}{\sqrt{\sec \left(a+b \log \left(c x^n\right)\right)}} \, dx","Int[1/Sqrt[Sec[a + b*Log[c*x^n]]],x]","\frac{2 x \, _2F_1\left(-\frac{1}{2},-\frac{b n+2 i}{4 b n};\frac{1}{4} \left(3-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2-i b n) \sqrt{1+e^{2 i a} \left(c x^n\right)^{2 i b}} \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)}}","\frac{2 x \, _2F_1\left(-\frac{1}{2},-\frac{b n+2 i}{4 b n};\frac{1}{4} \left(3-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2-i b n) \sqrt{1+e^{2 i a} \left(c x^n\right)^{2 i b}} \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)}}",1,"(2*x*Hypergeometric2F1[-1/2, -(2*I + b*n)/(4*b*n), (3 - (2*I)/(b*n))/4, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((2 - I*b*n)*Sqrt[1 + E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Sqrt[Sec[a + b*Log[c*x^n]]])","A",3,3,15,0.2000,1,"{4503, 4507, 364}"
273,1,54,0,0.0440065,"\int \frac{1}{x \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)}} \, dx","Int[1/(x*Sqrt[Sec[a + b*Log[c*x^n]]]),x]","\frac{2 \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)} \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}","\frac{2 \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)} \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}",1,"(2*Sqrt[Cos[a + b*Log[c*x^n]]]*EllipticE[(a + b*Log[c*x^n])/2, 2]*Sqrt[Sec[a + b*Log[c*x^n]]])/(b*n)","A",3,2,19,0.1053,1,"{3771, 2639}"
274,1,109,0,0.0702157,"\int \frac{1}{\sec ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[Sec[a + b*Log[c*x^n]]^(-3/2),x]","\frac{2 x \, _2F_1\left(-\frac{3}{2},\frac{1}{4} \left(-3-\frac{2 i}{b n}\right);\frac{1}{4} \left(1-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2-3 i b n) \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \sec ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}","\frac{2 x \, _2F_1\left(-\frac{3}{2},\frac{1}{4} \left(-3-\frac{2 i}{b n}\right);\frac{1}{4} \left(1-\frac{2 i}{b n}\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2-3 i b n) \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \sec ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}",1,"(2*x*Hypergeometric2F1[-3/2, (-3 - (2*I)/(b*n))/4, (1 - (2*I)/(b*n))/4, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((2 - (3*I)*b*n)*(1 + E^((2*I)*a)*(c*x^n)^((2*I)*b))^(3/2)*Sec[a + b*Log[c*x^n]]^(3/2))","A",3,3,15,0.2000,1,"{4503, 4507, 364}"
275,1,93,0,0.0603745,"\int \frac{1}{x \sec ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[1/(x*Sec[a + b*Log[c*x^n]]^(3/2)),x]","\frac{2 \sin \left(a+b \log \left(c x^n\right)\right)}{3 b n \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)}}+\frac{2 \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)} \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{3 b n}","\frac{2 \sin \left(a+b \log \left(c x^n\right)\right)}{3 b n \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)}}+\frac{2 \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)} \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{3 b n}",1,"(2*Sqrt[Cos[a + b*Log[c*x^n]]]*EllipticF[(a + b*Log[c*x^n])/2, 2]*Sqrt[Sec[a + b*Log[c*x^n]]])/(3*b*n) + (2*Sin[a + b*Log[c*x^n]])/(3*b*n*Sqrt[Sec[a + b*Log[c*x^n]]])","A",4,3,19,0.1579,1,"{3769, 3771, 2641}"
276,1,110,0,0.0724982,"\int \frac{1}{\sec ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[Sec[a + b*Log[c*x^n]]^(-5/2),x]","\frac{2 x \, _2F_1\left(-\frac{5}{2},\frac{1}{4} \left(-5-\frac{2 i}{b n}\right);-\frac{b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2-5 i b n) \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2} \sec ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}","\frac{2 x \, _2F_1\left(-\frac{5}{2},\frac{1}{4} \left(-5-\frac{2 i}{b n}\right);-\frac{b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2-5 i b n) \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2} \sec ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}",1,"(2*x*Hypergeometric2F1[-5/2, (-5 - (2*I)/(b*n))/4, -(2*I + b*n)/(4*b*n), -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((2 - (5*I)*b*n)*(1 + E^((2*I)*a)*(c*x^n)^((2*I)*b))^(5/2)*Sec[a + b*Log[c*x^n]]^(5/2))","A",3,3,15,0.2000,1,"{4503, 4507, 364}"
277,1,93,0,0.061194,"\int \frac{1}{x \sec ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[1/(x*Sec[a + b*Log[c*x^n]]^(5/2)),x]","\frac{2 \sin \left(a+b \log \left(c x^n\right)\right)}{5 b n \sec ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}+\frac{6 \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)} \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{5 b n}","\frac{2 \sin \left(a+b \log \left(c x^n\right)\right)}{5 b n \sec ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}+\frac{6 \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)} \sqrt{\cos \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{5 b n}",1,"(6*Sqrt[Cos[a + b*Log[c*x^n]]]*EllipticE[(a + b*Log[c*x^n])/2, 2]*Sqrt[Sec[a + b*Log[c*x^n]]])/(5*b*n) + (2*Sin[a + b*Log[c*x^n]])/(5*b*n*Sec[a + b*Log[c*x^n]]^(3/2))","A",4,3,19,0.1579,1,"{3769, 3771, 2639}"
278,1,102,0,0.0886081,"\int x^m \sec ^3\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^m*Sec[a + b*Log[c*x^n]]^3,x]","\frac{8 e^{3 i a} x^{m+1} \left(c x^n\right)^{3 i b} \, _2F_1\left(3,-\frac{i (m+1)-3 b n}{2 b n};-\frac{i (m+1)-5 b n}{2 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{3 i b n+m+1}","\frac{8 e^{3 i a} x^{m+1} \left(c x^n\right)^{3 i b} \, _2F_1\left(3,-\frac{i (m+1)-3 b n}{2 b n};-\frac{i (m+1)-5 b n}{2 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{3 i b n+m+1}",1,"(8*E^((3*I)*a)*x^(1 + m)*(c*x^n)^((3*I)*b)*Hypergeometric2F1[3, -(I*(1 + m) - 3*b*n)/(2*b*n), -(I*(1 + m) - 5*b*n)/(2*b*n), -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/(1 + m + (3*I)*b*n)","A",3,3,17,0.1765,1,"{4509, 4505, 364}"
279,1,102,0,0.0846519,"\int x^m \sec ^2\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^m*Sec[a + b*Log[c*x^n]]^2,x]","\frac{4 e^{2 i a} x^{m+1} \left(c x^n\right)^{2 i b} \, _2F_1\left(2,-\frac{i (m+1)-2 b n}{2 b n};-\frac{i (m+1)-4 b n}{2 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{2 i b n+m+1}","\frac{4 e^{2 i a} x^{m+1} \left(c x^n\right)^{2 i b} \, _2F_1\left(2,-\frac{i (m+1)-2 b n}{2 b n};-\frac{i (m+1)-4 b n}{2 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{2 i b n+m+1}",1,"(4*E^((2*I)*a)*x^(1 + m)*(c*x^n)^((2*I)*b)*Hypergeometric2F1[2, -(I*(1 + m) - 2*b*n)/(2*b*n), -(I*(1 + m) - 4*b*n)/(2*b*n), -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/(1 + m + (2*I)*b*n)","A",3,3,17,0.1765,1,"{4509, 4505, 364}"
280,1,99,0,0.0686398,"\int x^m \sec \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^m*Sec[a + b*Log[c*x^n]],x]","\frac{2 e^{i a} x^{m+1} \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1-\frac{i (m+1)}{b n}\right);-\frac{i (m+1)-3 b n}{2 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{i b n+m+1}","\frac{2 e^{i a} x^{m+1} \left(c x^n\right)^{i b} \, _2F_1\left(1,-\frac{i m-b n+i}{2 b n};-\frac{i (m+1)-3 b n}{2 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{i b n+m+1}",1,"(2*E^(I*a)*x^(1 + m)*(c*x^n)^(I*b)*Hypergeometric2F1[1, (1 - (I*(1 + m))/(b*n))/2, -(I*(1 + m) - 3*b*n)/(2*b*n), -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/(1 + m + I*b*n)","A",3,3,15,0.2000,1,"{4509, 4505, 364}"
281,1,126,0,0.0991482,"\int x^m \sec ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^m*Sec[a + b*Log[c*x^n]]^(5/2),x]","\frac{2 x^{m+1} \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2} \, _2F_1\left(\frac{5}{2},\frac{1}{4} \left(5-\frac{2 i (m+1)}{b n}\right);-\frac{2 i m-9 b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sec ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{5 i b n+2 m+2}","\frac{2 x^{m+1} \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2} \, _2F_1\left(\frac{5}{2},-\frac{2 i m-5 b n+2 i}{4 b n};-\frac{2 i m-9 b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sec ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{5 i b n+2 m+2}",1,"(2*x^(1 + m)*(1 + E^((2*I)*a)*(c*x^n)^((2*I)*b))^(5/2)*Hypergeometric2F1[5/2, (5 - ((2*I)*(1 + m))/(b*n))/4, -(2*I + (2*I)*m - 9*b*n)/(4*b*n), -(E^((2*I)*a)*(c*x^n)^((2*I)*b))]*Sec[a + b*Log[c*x^n]]^(5/2))/(2 + 2*m + (5*I)*b*n)","A",3,3,19,0.1579,1,"{4509, 4507, 364}"
282,1,126,0,0.0955526,"\int x^m \sec ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^m*Sec[a + b*Log[c*x^n]]^(3/2),x]","\frac{2 x^{m+1} \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{1}{4} \left(3-\frac{2 i (m+1)}{b n}\right);-\frac{2 i m-7 b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sec ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{3 i b n+2 m+2}","\frac{2 x^{m+1} \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \, _2F_1\left(\frac{3}{2},-\frac{2 i m-3 b n+2 i}{4 b n};-\frac{2 i m-7 b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sec ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{3 i b n+2 m+2}",1,"(2*x^(1 + m)*(1 + E^((2*I)*a)*(c*x^n)^((2*I)*b))^(3/2)*Hypergeometric2F1[3/2, (3 - ((2*I)*(1 + m))/(b*n))/4, -(2*I + (2*I)*m - 7*b*n)/(4*b*n), -(E^((2*I)*a)*(c*x^n)^((2*I)*b))]*Sec[a + b*Log[c*x^n]]^(3/2))/(2 + 2*m + (3*I)*b*n)","A",3,3,19,0.1579,1,"{4509, 4507, 364}"
283,1,130,0,0.0914406,"\int x^m \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)} \, dx","Int[x^m*Sqrt[Sec[a + b*Log[c*x^n]]],x]","\frac{2 x^{m+1} \sqrt{1+e^{2 i a} \left(c x^n\right)^{2 i b}} \, _2F_1\left(\frac{1}{2},-\frac{2 i m-b n+2 i}{4 b n};-\frac{2 i m-5 b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)}}{i b n+2 m+2}","\frac{2 x^{m+1} \sqrt{1+e^{2 i a} \left(c x^n\right)^{2 i b}} \, _2F_1\left(\frac{1}{2},-\frac{2 i m-b n+2 i}{4 b n};-\frac{2 i m-5 b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)}}{i b n+2 m+2}",1,"(2*x^(1 + m)*Sqrt[1 + E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Hypergeometric2F1[1/2, -(2*I + (2*I)*m - b*n)/(4*b*n), -(2*I + (2*I)*m - 5*b*n)/(4*b*n), -(E^((2*I)*a)*(c*x^n)^((2*I)*b))]*Sqrt[Sec[a + b*Log[c*x^n]]])/(2 + 2*m + I*b*n)","A",3,3,19,0.1579,1,"{4509, 4507, 364}"
284,1,126,0,0.0919304,"\int \frac{x^m}{\sqrt{\sec \left(a+b \log \left(c x^n\right)\right)}} \, dx","Int[x^m/Sqrt[Sec[a + b*Log[c*x^n]]],x]","\frac{2 x^{m+1} \, _2F_1\left(-\frac{1}{2},\frac{1}{4} \left(-\frac{2 i (m+1)}{b n}-1\right);-\frac{2 i m-3 b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(-i b n+2 m+2) \sqrt{1+e^{2 i a} \left(c x^n\right)^{2 i b}} \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)}}","\frac{2 x^{m+1} \, _2F_1\left(-\frac{1}{2},-\frac{2 i m+b n+2 i}{4 b n};-\frac{2 i m-3 b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(-i b n+2 m+2) \sqrt{1+e^{2 i a} \left(c x^n\right)^{2 i b}} \sqrt{\sec \left(a+b \log \left(c x^n\right)\right)}}",1,"(2*x^(1 + m)*Hypergeometric2F1[-1/2, (-1 - ((2*I)*(1 + m))/(b*n))/4, -(2*I + (2*I)*m - 3*b*n)/(4*b*n), -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((2 + 2*m - I*b*n)*Sqrt[1 + E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Sqrt[Sec[a + b*Log[c*x^n]]])","A",3,3,19,0.1579,1,"{4509, 4507, 364}"
285,1,126,0,0.0959615,"\int \frac{x^m}{\sec ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[x^m/Sec[a + b*Log[c*x^n]]^(3/2),x]","\frac{2 x^{m+1} \, _2F_1\left(-\frac{3}{2},\frac{1}{4} \left(-\frac{2 i (m+1)}{b n}-3\right);-\frac{2 i m-b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(-3 i b n+2 m+2) \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \sec ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}","\frac{2 x^{m+1} \, _2F_1\left(-\frac{3}{2},-\frac{2 i m+3 b n+2 i}{4 b n};-\frac{2 i m-b n+2 i}{4 b n};-e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(-3 i b n+2 m+2) \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \sec ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}",1,"(2*x^(1 + m)*Hypergeometric2F1[-3/2, (-3 - ((2*I)*(1 + m))/(b*n))/4, -(2*I + (2*I)*m - b*n)/(4*b*n), -(E^((2*I)*a)*(c*x^n)^((2*I)*b))])/((2 + 2*m - (3*I)*b*n)*(1 + E^((2*I)*a)*(c*x^n)^((2*I)*b))^(3/2)*Sec[a + b*Log[c*x^n]]^(3/2))","A",3,3,19,0.1579,1,"{4509, 4507, 364}"
286,1,133,0,0.1214905,"\int (e x)^m \sec ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Sec[d*(a + b*Log[c*x^n])]^p,x]","\frac{(e x)^{m+1} \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^p \, _2F_1\left(p,\frac{1}{2} \left(p-\frac{i (m+1)}{b d n}\right);\frac{1}{2} \left(-\frac{i (m+1)}{b d n}+p+2\right);-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right) \sec ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e (i b d n p+m+1)}","\frac{(e x)^{m+1} \left(1+e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^p \, _2F_1\left(p,-\frac{i m-b d n p+i}{2 b d n};\frac{1}{2} \left(-\frac{i (m+1)}{b d n}+p+2\right);-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right) \sec ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e (i b d n p+m+1)}",1,"((e*x)^(1 + m)*(1 + E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d))^p*Hypergeometric2F1[p, (((-I)*(1 + m))/(b*d*n) + p)/2, (2 - (I*(1 + m))/(b*d*n) + p)/2, -(E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d))]*Sec[d*(a + b*Log[c*x^n])]^p)/(e*(1 + m + I*b*d*n*p))","A",3,3,21,0.1429,1,"{4509, 4507, 364}"
287,1,106,0,0.0827361,"\int x \sec ^p\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Sec[a + b*Log[c*x^n]]^p,x]","\frac{x^2 \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^p \, _2F_1\left(p,\frac{1}{2} \left(p-\frac{2 i}{b n}\right);\frac{1}{2} \left(p-\frac{2 i}{b n}+2\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sec ^p\left(a+b \log \left(c x^n\right)\right)}{2+i b n p}","\frac{x^2 \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^p \, _2F_1\left(p,\frac{1}{2} \left(p-\frac{2 i}{b n}\right);\frac{1}{2} \left(p-\frac{2 i}{b n}+2\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sec ^p\left(a+b \log \left(c x^n\right)\right)}{2+i b n p}",1,"(x^2*(1 + E^((2*I)*a)*(c*x^n)^((2*I)*b))^p*Hypergeometric2F1[p, ((-2*I)/(b*n) + p)/2, (2 - (2*I)/(b*n) + p)/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))]*Sec[a + b*Log[c*x^n]]^p)/(2 + I*b*n*p)","A",3,3,15,0.2000,1,"{4509, 4507, 364}"
288,1,107,0,0.0694251,"\int \sec ^p\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sec[a + b*Log[c*x^n]]^p,x]","\frac{x \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^p \, _2F_1\left(p,-\frac{i-b n p}{2 b n};\frac{1}{2} \left(p-\frac{i}{b n}+2\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sec ^p\left(a+b \log \left(c x^n\right)\right)}{1+i b n p}","\frac{x \left(1+e^{2 i a} \left(c x^n\right)^{2 i b}\right)^p \, _2F_1\left(p,-\frac{i-b n p}{2 b n};\frac{1}{2} \left(p-\frac{i}{b n}+2\right);-e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sec ^p\left(a+b \log \left(c x^n\right)\right)}{1+i b n p}",1,"(x*(1 + E^((2*I)*a)*(c*x^n)^((2*I)*b))^p*Hypergeometric2F1[p, -(I - b*n*p)/(2*b*n), (2 - I/(b*n) + p)/2, -(E^((2*I)*a)*(c*x^n)^((2*I)*b))]*Sec[a + b*Log[c*x^n]]^p)/(1 + I*b*n*p)","A",3,3,13,0.2308,1,"{4503, 4507, 364}"
289,1,86,0,0.0618108,"\int x^2 \csc \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*Csc[a + b*Log[c*x^n]],x]","\frac{2 e^{i a} x^3 \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1-\frac{3 i}{b n}\right);\frac{3}{2} \left(1-\frac{i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{-b n+3 i}","\frac{2 e^{i a} x^3 \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1-\frac{3 i}{b n}\right);\frac{3}{2} \left(1-\frac{i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{-b n+3 i}",1,"(2*E^(I*a)*x^3*(c*x^n)^(I*b)*Hypergeometric2F1[1, (1 - (3*I)/(b*n))/2, (3*(1 - I/(b*n)))/2, E^((2*I)*a)*(c*x^n)^((2*I)*b)])/(3*I - b*n)","A",3,3,15,0.2000,1,"{4510, 4506, 364}"
290,1,86,0,0.0557441,"\int x \csc \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Csc[a + b*Log[c*x^n]],x]","\frac{2 e^{i a} x^2 \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1-\frac{2 i}{b n}\right);\frac{1}{2} \left(3-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{-b n+2 i}","\frac{2 e^{i a} x^2 \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1-\frac{2 i}{b n}\right);\frac{1}{2} \left(3-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{-b n+2 i}",1,"(2*E^(I*a)*x^2*(c*x^n)^(I*b)*Hypergeometric2F1[1, (1 - (2*I)/(b*n))/2, (3 - (2*I)/(b*n))/2, E^((2*I)*a)*(c*x^n)^((2*I)*b)])/(2*I - b*n)","A",3,3,13,0.2308,1,"{4510, 4506, 364}"
291,1,84,0,0.0507095,"\int \csc \left(a+b \log \left(c x^n\right)\right) \, dx","Int[Csc[a + b*Log[c*x^n]],x]","\frac{2 e^{i a} x \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1-\frac{i}{b n}\right);\frac{1}{2} \left(3-\frac{i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{-b n+i}","\frac{2 e^{i a} x \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1-\frac{i}{b n}\right);\frac{1}{2} \left(3-\frac{i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{-b n+i}",1,"(2*E^(I*a)*x*(c*x^n)^(I*b)*Hypergeometric2F1[1, (1 - I/(b*n))/2, (3 - I/(b*n))/2, E^((2*I)*a)*(c*x^n)^((2*I)*b)])/(I - b*n)","A",3,3,11,0.2727,1,"{4504, 4506, 364}"
292,1,20,0,0.015723,"\int \frac{\csc \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Csc[a + b*Log[c*x^n]]/x,x]","-\frac{\tanh ^{-1}\left(\cos \left(a+b \log \left(c x^n\right)\right)\right)}{b n}","-\frac{\tanh ^{-1}\left(\cos \left(a+b \log \left(c x^n\right)\right)\right)}{b n}",1,"-(ArcTanh[Cos[a + b*Log[c*x^n]]]/(b*n))","A",2,1,15,0.06667,1,"{3770}"
293,1,85,0,0.059023,"\int \frac{\csc \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[Csc[a + b*Log[c*x^n]]/x^2,x]","-\frac{2 e^{i a} \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1+\frac{i}{b n}\right);\frac{1}{2} \left(3+\frac{i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x (b n+i)}","-\frac{2 e^{i a} \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1+\frac{i}{b n}\right);\frac{1}{2} \left(3+\frac{i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x (b n+i)}",1,"(-2*E^(I*a)*(c*x^n)^(I*b)*Hypergeometric2F1[1, (1 + I/(b*n))/2, (3 + I/(b*n))/2, E^((2*I)*a)*(c*x^n)^((2*I)*b)])/((I + b*n)*x)","A",3,3,15,0.2000,1,"{4510, 4506, 364}"
294,1,85,0,0.0585942,"\int \frac{\csc \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[Csc[a + b*Log[c*x^n]]/x^3,x]","-\frac{2 e^{i a} \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1+\frac{2 i}{b n}\right);\frac{1}{2} \left(3+\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x^2 (b n+2 i)}","-\frac{2 e^{i a} \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1+\frac{2 i}{b n}\right);\frac{1}{2} \left(3+\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{x^2 (b n+2 i)}",1,"(-2*E^(I*a)*(c*x^n)^(I*b)*Hypergeometric2F1[1, (1 + (2*I)/(b*n))/2, (3 + (2*I)/(b*n))/2, E^((2*I)*a)*(c*x^n)^((2*I)*b)])/((2*I + b*n)*x^2)","A",3,3,15,0.2000,1,"{4510, 4506, 364}"
295,1,84,0,0.0599466,"\int \csc ^2\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Csc[a + b*Log[c*x^n]]^2,x]","-\frac{4 e^{2 i a} x \left(c x^n\right)^{2 i b} \, _2F_1\left(2,\frac{1}{2} \left(2-\frac{i}{b n}\right);\frac{1}{2} \left(4-\frac{i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{1+2 i b n}","-\frac{4 e^{2 i a} x \left(c x^n\right)^{2 i b} \, _2F_1\left(2,\frac{1}{2} \left(2-\frac{i}{b n}\right);\frac{1}{2} \left(4-\frac{i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{1+2 i b n}",1,"(-4*E^((2*I)*a)*x*(c*x^n)^((2*I)*b)*Hypergeometric2F1[2, (2 - I/(b*n))/2, (4 - I/(b*n))/2, E^((2*I)*a)*(c*x^n)^((2*I)*b)])/(1 + (2*I)*b*n)","A",3,3,13,0.2308,1,"{4504, 4506, 364}"
296,1,19,0,0.0279832,"\int \frac{\csc ^2\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Csc[a + b*Log[c*x^n]]^2/x,x]","-\frac{\cot \left(a+b \log \left(c x^n\right)\right)}{b n}","-\frac{\cot \left(a+b \log \left(c x^n\right)\right)}{b n}",1,"-(Cot[a + b*Log[c*x^n]]/(b*n))","A",3,2,17,0.1176,1,"{3767, 8}"
297,1,84,0,0.0622205,"\int \csc ^3\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Csc[a + b*Log[c*x^n]]^3,x]","-\frac{8 e^{3 i a} x \left(c x^n\right)^{3 i b} \, _2F_1\left(3,\frac{1}{2} \left(3-\frac{i}{b n}\right);\frac{1}{2} \left(5-\frac{i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{-3 b n+i}","-\frac{8 e^{3 i a} x \left(c x^n\right)^{3 i b} \, _2F_1\left(3,\frac{1}{2} \left(3-\frac{i}{b n}\right);\frac{1}{2} \left(5-\frac{i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{-3 b n+i}",1,"(-8*E^((3*I)*a)*x*(c*x^n)^((3*I)*b)*Hypergeometric2F1[3, (3 - I/(b*n))/2, (5 - I/(b*n))/2, E^((2*I)*a)*(c*x^n)^((2*I)*b)])/(I - 3*b*n)","A",3,3,13,0.2308,1,"{4504, 4506, 364}"
298,1,55,0,0.0395494,"\int \frac{\csc ^3\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Csc[a + b*Log[c*x^n]]^3/x,x]","-\frac{\tanh ^{-1}\left(\cos \left(a+b \log \left(c x^n\right)\right)\right)}{2 b n}-\frac{\cot \left(a+b \log \left(c x^n\right)\right) \csc \left(a+b \log \left(c x^n\right)\right)}{2 b n}","-\frac{\tanh ^{-1}\left(\cos \left(a+b \log \left(c x^n\right)\right)\right)}{2 b n}-\frac{\cot \left(a+b \log \left(c x^n\right)\right) \csc \left(a+b \log \left(c x^n\right)\right)}{2 b n}",1,"-ArcTanh[Cos[a + b*Log[c*x^n]]]/(2*b*n) - (Cot[a + b*Log[c*x^n]]*Csc[a + b*Log[c*x^n]])/(2*b*n)","A",3,2,17,0.1176,1,"{3768, 3770}"
299,1,84,0,0.0610124,"\int \csc ^4\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Csc[a + b*Log[c*x^n]]^4,x]","\frac{16 e^{4 i a} x \left(c x^n\right)^{4 i b} \, _2F_1\left(4,\frac{1}{2} \left(4-\frac{i}{b n}\right);\frac{1}{2} \left(6-\frac{i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{1+4 i b n}","\frac{16 e^{4 i a} x \left(c x^n\right)^{4 i b} \, _2F_1\left(4,\frac{1}{2} \left(4-\frac{i}{b n}\right);\frac{1}{2} \left(6-\frac{i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{1+4 i b n}",1,"(16*E^((4*I)*a)*x*(c*x^n)^((4*I)*b)*Hypergeometric2F1[4, (4 - I/(b*n))/2, (6 - I/(b*n))/2, E^((2*I)*a)*(c*x^n)^((2*I)*b)])/(1 + (4*I)*b*n)","A",3,3,13,0.2308,1,"{4504, 4506, 364}"
300,1,43,0,0.0340999,"\int \frac{\csc ^4\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Csc[a + b*Log[c*x^n]]^4/x,x]","-\frac{\cot ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}-\frac{\cot \left(a+b \log \left(c x^n\right)\right)}{b n}","-\frac{\cot ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}-\frac{\cot \left(a+b \log \left(c x^n\right)\right)}{b n}",1,"-(Cot[a + b*Log[c*x^n]]/(b*n)) - Cot[a + b*Log[c*x^n]]^3/(3*b*n)","A",3,1,17,0.05882,1,"{3767}"
301,1,172,0,0.1265809,"\int \left(-\left(1+b^2 n^2\right) \csc \left(a+b \log \left(c x^n\right)\right)+2 b^2 n^2 \csc ^3\left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[-((1 + b^2*n^2)*Csc[a + b*Log[c*x^n]]) + 2*b^2*n^2*Csc[a + b*Log[c*x^n]]^3,x]","2 e^{i a} x (b n+i) \left(c x^n\right)^{i b} \, _2F_1\left(1,\frac{1}{2} \left(1-\frac{i}{b n}\right);\frac{1}{2} \left(3-\frac{i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)-\frac{16 e^{3 i a} b^2 n^2 x \left(c x^n\right)^{3 i b} \, _2F_1\left(3,\frac{1}{2} \left(3-\frac{i}{b n}\right);\frac{1}{2} \left(5-\frac{i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{-3 b n+i}","-x \csc \left(a+b \log \left(c x^n\right)\right)-b n x \cot \left(a+b \log \left(c x^n\right)\right) \csc \left(a+b \log \left(c x^n\right)\right)",1,"2*E^(I*a)*(I + b*n)*x*(c*x^n)^(I*b)*Hypergeometric2F1[1, (1 - I/(b*n))/2, (3 - I/(b*n))/2, E^((2*I)*a)*(c*x^n)^((2*I)*b)] - (16*b^2*E^((3*I)*a)*n^2*x*(c*x^n)^((3*I)*b)*Hypergeometric2F1[3, (3 - I/(b*n))/2, (5 - I/(b*n))/2, E^((2*I)*a)*(c*x^n)^((2*I)*b)])/(I - 3*b*n)","C",7,3,44,0.06818,0,"{4504, 4506, 364}"
302,1,142,0,0.1836751,"\int x^m \csc ^3\left(a+2 \log \left(c x^{\frac{1}{2} \sqrt{-(1+m)^2}}\right)\right) \, dx","Int[x^m*Csc[a + 2*Log[c*x^(Sqrt[-(1 + m)^2]/2)]]^3,x]","-\frac{8 e^{3 i a} x^{m+1} \left(c x^{\frac{1}{2} \sqrt{-(m+1)^2}}\right)^{6 i} \, _2F_1\left(3,\frac{1}{2} \left(3-\frac{i (m+1)}{\sqrt{-(m+1)^2}}\right);\frac{1}{2} \left(5-\frac{i (m+1)}{\sqrt{-(m+1)^2}}\right);e^{2 i a} \left(c x^{\frac{1}{2} \sqrt{-(m+1)^2}}\right)^{4 i}\right)}{i m-3 \sqrt{-(m+1)^2}+i}","\frac{x^{m+1} \csc \left(a+2 \log \left(c x^{\frac{1}{2} \sqrt{-(m+1)^2}}\right)\right)}{2 (m+1)}-\frac{x^{m+1} \cot \left(a+2 \log \left(c x^{\frac{1}{2} \sqrt{-(m+1)^2}}\right)\right) \csc \left(a+2 \log \left(c x^{\frac{1}{2} \sqrt{-(m+1)^2}}\right)\right)}{2 \sqrt{-(m+1)^2}}",1,"(-8*E^((3*I)*a)*x^(1 + m)*(c*x^(Sqrt[-(1 + m)^2]/2))^(6*I)*Hypergeometric2F1[3, (3 - (I*(1 + m))/Sqrt[-(1 + m)^2])/2, (5 - (I*(1 + m))/Sqrt[-(1 + m)^2])/2, E^((2*I)*a)*(c*x^(Sqrt[-(1 + m)^2]/2))^(4*I)])/(I + I*m - 3*Sqrt[-(1 + m)^2])","C",3,3,31,0.09677,0,"{4510, 4506, 364}"
303,1,49,0,0.0422573,"\int x \csc ^3\left(a+2 \log \left(c x^i\right)\right) \, dx","Int[x*Csc[a + 2*Log[c*x^I]]^3,x]","-\frac{i e^{i a} x^2 \left(c x^i\right)^{2 i}}{\left(1-e^{2 i a} \left(c x^i\right)^{4 i}\right)^2}","-\frac{i e^{i a} x^2 \left(c x^i\right)^{2 i}}{\left(1-e^{2 i a} \left(c x^i\right)^{4 i}\right)^2}",1,"((-I)*E^(I*a)*(c*x^I)^(2*I)*x^2)/(1 - E^((2*I)*a)*(c*x^I)^(4*I))^2","A",3,3,17,0.1765,1,"{4510, 4506, 261}"
304,1,51,0,0.0352578,"\int \csc ^3\left(a+2 \log \left(c x^{\frac{i}{2}}\right)\right) \, dx","Int[Csc[a + 2*Log[c*x^(I/2)]]^3,x]","-\frac{2 i e^{i a} x \left(c x^{\frac{i}{2}}\right)^{2 i}}{\left(1-e^{2 i a} \left(c x^{\frac{i}{2}}\right)^{4 i}\right)^2}","\frac{1}{2} x \csc \left(a+2 \log \left(c x^{\frac{i}{2}}\right)\right)+\frac{1}{2} i x \cot \left(a+2 \log \left(c x^{\frac{i}{2}}\right)\right) \csc \left(a+2 \log \left(c x^{\frac{i}{2}}\right)\right)",1,"((-2*I)*E^(I*a)*(c*x^(I/2))^(2*I)*x)/(1 - E^((2*I)*a)*(c*x^(I/2))^(4*I))^2","A",3,3,17,0.1765,0,"{4504, 4506, 261}"
305,1,51,0,0.0403293,"\int \csc ^3\left(a+2 \log \left(c x^{-\frac{i}{2}}\right)\right) \, dx","Int[Csc[a + 2*Log[c/x^(I/2)]]^3,x]","\frac{2 i e^{3 i a} x \left(c x^{-\frac{i}{2}}\right)^{6 i}}{\left(1-e^{2 i a} \left(c x^{-\frac{i}{2}}\right)^{4 i}\right)^2}","\frac{2 i e^{3 i a} x \left(c x^{-\frac{i}{2}}\right)^{6 i}}{\left(1-e^{2 i a} \left(c x^{-\frac{i}{2}}\right)^{4 i}\right)^2}",1,"((2*I)*E^((3*I)*a)*(c/x^(I/2))^(6*I)*x)/(1 - E^((2*I)*a)*(c/x^(I/2))^(4*I))^2","A",3,3,17,0.1765,1,"{4504, 4506, 264}"
306,1,96,0,0.0883863,"\int \csc ^p\left(a+\frac{i \log \left(c x^n\right)}{n (-2+p)}\right) \, dx","Int[Csc[a + (I*Log[c*x^n])/(n*(-2 + p))]^p,x]","-\frac{e^{-2 i a} (2-p) x \left(c x^n\right)^{-\frac{2}{n (2-p)}} \left(1-e^{2 i a} \left(c x^n\right)^{\frac{2}{n (2-p)}}\right) \csc ^p\left(a-\frac{i \log \left(c x^n\right)}{n (2-p)}\right)}{2 (1-p)}","-\frac{e^{-2 i a} (2-p) x \left(c x^n\right)^{-\frac{2}{n (2-p)}} \left(1-e^{2 i a} \left(c x^n\right)^{\frac{2}{n (2-p)}}\right) \csc ^p\left(a-\frac{i \log \left(c x^n\right)}{n (2-p)}\right)}{2 (1-p)}",1,"-((2 - p)*x*(1 - E^((2*I)*a)*(c*x^n)^(2/(n*(2 - p))))*Csc[a - (I*Log[c*x^n])/(n*(2 - p))]^p)/(2*E^((2*I)*a)*(1 - p)*(c*x^n)^(2/(n*(2 - p))))","A",3,3,23,0.1304,1,"{4504, 4508, 261}"
307,1,71,0,0.0759444,"\int \csc ^p\left(a-\frac{i \log \left(c x^n\right)}{n (-2+p)}\right) \, dx","Int[Csc[a - (I*Log[c*x^n])/(n*(-2 + p))]^p,x]","\frac{(2-p) x \left(1-e^{2 i a} \left(c x^n\right)^{-\frac{2}{n (2-p)}}\right) \csc ^p\left(a+\frac{i \log \left(c x^n\right)}{n (2-p)}\right)}{2 (1-p)}","\frac{(2-p) x \left(1-e^{2 i a} \left(c x^n\right)^{-\frac{2}{n (2-p)}}\right) \csc ^p\left(a+\frac{i \log \left(c x^n\right)}{n (2-p)}\right)}{2 (1-p)}",1,"((2 - p)*x*(1 - E^((2*I)*a)/(c*x^n)^(2/(n*(2 - p))))*Csc[a + (I*Log[c*x^n])/(n*(2 - p))]^p)/(2*(1 - p))","A",3,3,23,0.1304,1,"{4504, 4508, 264}"
308,1,109,0,0.0705614,"\int \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)} \, dx","Int[Sqrt[Csc[a + b*Log[c*x^n]]],x]","\frac{2 x \sqrt{1-e^{2 i a} \left(c x^n\right)^{2 i b}} \, _2F_1\left(\frac{1}{2},\frac{1}{4} \left(1-\frac{2 i}{b n}\right);\frac{1}{4} \left(5-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)}}{2+i b n}","\frac{2 x \sqrt{1-e^{2 i a} \left(c x^n\right)^{2 i b}} \, _2F_1\left(\frac{1}{2},\frac{1}{4} \left(1-\frac{2 i}{b n}\right);\frac{1}{4} \left(5-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)}}{2+i b n}",1,"(2*x*Sqrt[1 - E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Sqrt[Csc[a + b*Log[c*x^n]]]*Hypergeometric2F1[1/2, (1 - (2*I)/(b*n))/4, (5 - (2*I)/(b*n))/4, E^((2*I)*a)*(c*x^n)^((2*I)*b)])/(2 + I*b*n)","A",3,3,15,0.2000,1,"{4504, 4508, 364}"
309,1,59,0,0.0412643,"\int \frac{\sqrt{\csc \left(a+b \log \left(c x^n\right)\right)}}{x} \, dx","Int[Sqrt[Csc[a + b*Log[c*x^n]]]/x,x]","\frac{2 \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)} \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{b n}","\frac{2 \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)} \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{b n}",1,"(2*Sqrt[Csc[a + b*Log[c*x^n]]]*EllipticF[(a - Pi/2 + b*Log[c*x^n])/2, 2]*Sqrt[Sin[a + b*Log[c*x^n]]])/(b*n)","A",3,2,19,0.1053,1,"{3771, 2641}"
310,1,109,0,0.0701248,"\int \csc ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Csc[a + b*Log[c*x^n]]^(3/2),x]","\frac{2 x \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{1}{4} \left(3-\frac{2 i}{b n}\right);\frac{1}{4} \left(7-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \csc ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{2+3 i b n}","\frac{2 x \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{1}{4} \left(3-\frac{2 i}{b n}\right);\frac{1}{4} \left(7-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \csc ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{2+3 i b n}",1,"(2*x*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^(3/2)*Csc[a + b*Log[c*x^n]]^(3/2)*Hypergeometric2F1[3/2, (3 - (2*I)/(b*n))/4, (7 - (2*I)/(b*n))/4, E^((2*I)*a)*(c*x^n)^((2*I)*b)])/(2 + (3*I)*b*n)","A",3,3,15,0.2000,1,"{4504, 4508, 364}"
311,1,94,0,0.0549318,"\int \frac{\csc ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Csc[a + b*Log[c*x^n]]^(3/2)/x,x]","-\frac{2 \cos \left(a+b \log \left(c x^n\right)\right) \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)}}{b n}-\frac{2 \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)} \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{b n}","-\frac{2 \cos \left(a+b \log \left(c x^n\right)\right) \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)}}{b n}-\frac{2 \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)} \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{b n}",1,"(-2*Cos[a + b*Log[c*x^n]]*Sqrt[Csc[a + b*Log[c*x^n]]])/(b*n) - (2*Sqrt[Csc[a + b*Log[c*x^n]]]*EllipticE[(a - Pi/2 + b*Log[c*x^n])/2, 2]*Sqrt[Sin[a + b*Log[c*x^n]]])/(b*n)","A",4,3,19,0.1579,1,"{3768, 3771, 2639}"
312,1,109,0,0.0717096,"\int \csc ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Csc[a + b*Log[c*x^n]]^(5/2),x]","\frac{2 x \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2} \, _2F_1\left(\frac{5}{2},\frac{1}{4} \left(5-\frac{2 i}{b n}\right);\frac{1}{4} \left(9-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \csc ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{2+5 i b n}","\frac{2 x \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2} \, _2F_1\left(\frac{5}{2},\frac{1}{4} \left(5-\frac{2 i}{b n}\right);\frac{1}{4} \left(9-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \csc ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{2+5 i b n}",1,"(2*x*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^(5/2)*Csc[a + b*Log[c*x^n]]^(5/2)*Hypergeometric2F1[5/2, (5 - (2*I)/(b*n))/4, (9 - (2*I)/(b*n))/4, E^((2*I)*a)*(c*x^n)^((2*I)*b)])/(2 + (5*I)*b*n)","A",3,3,15,0.2000,1,"{4504, 4508, 364}"
313,1,98,0,0.0583563,"\int \frac{\csc ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Csc[a + b*Log[c*x^n]]^(5/2)/x,x]","\frac{2 \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)} \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{3 b n}-\frac{2 \cos \left(a+b \log \left(c x^n\right)\right) \csc ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{3 b n}","\frac{2 \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)} \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{3 b n}-\frac{2 \cos \left(a+b \log \left(c x^n\right)\right) \csc ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{3 b n}",1,"(-2*Cos[a + b*Log[c*x^n]]*Csc[a + b*Log[c*x^n]]^(3/2))/(3*b*n) + (2*Sqrt[Csc[a + b*Log[c*x^n]]]*EllipticF[(a - Pi/2 + b*Log[c*x^n])/2, 2]*Sqrt[Sin[a + b*Log[c*x^n]]])/(3*b*n)","A",4,3,19,0.1579,1,"{3768, 3771, 2641}"
314,1,110,0,0.0687148,"\int \frac{1}{\sqrt{\csc \left(a+b \log \left(c x^n\right)\right)}} \, dx","Int[1/Sqrt[Csc[a + b*Log[c*x^n]]],x]","\frac{2 x \, _2F_1\left(-\frac{1}{2},-\frac{b n+2 i}{4 b n};\frac{1}{4} \left(3-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2-i b n) \sqrt{1-e^{2 i a} \left(c x^n\right)^{2 i b}} \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)}}","\frac{2 x \, _2F_1\left(-\frac{1}{2},-\frac{b n+2 i}{4 b n};\frac{1}{4} \left(3-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2-i b n) \sqrt{1-e^{2 i a} \left(c x^n\right)^{2 i b}} \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)}}",1,"(2*x*Hypergeometric2F1[-1/2, -(2*I + b*n)/(4*b*n), (3 - (2*I)/(b*n))/4, E^((2*I)*a)*(c*x^n)^((2*I)*b)])/((2 - I*b*n)*Sqrt[1 - E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Sqrt[Csc[a + b*Log[c*x^n]]])","A",3,3,15,0.2000,1,"{4504, 4508, 364}"
315,1,59,0,0.0404361,"\int \frac{1}{x \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)}} \, dx","Int[1/(x*Sqrt[Csc[a + b*Log[c*x^n]]]),x]","\frac{2 \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)} \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{b n}","\frac{2 \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)} \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{b n}",1,"(2*Sqrt[Csc[a + b*Log[c*x^n]]]*EllipticE[(a - Pi/2 + b*Log[c*x^n])/2, 2]*Sqrt[Sin[a + b*Log[c*x^n]]])/(b*n)","A",3,2,19,0.1053,1,"{3771, 2639}"
316,1,109,0,0.0707769,"\int \frac{1}{\csc ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[Csc[a + b*Log[c*x^n]]^(-3/2),x]","\frac{2 x \, _2F_1\left(-\frac{3}{2},\frac{1}{4} \left(-3-\frac{2 i}{b n}\right);\frac{1}{4} \left(1-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2-3 i b n) \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \csc ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}","\frac{2 x \, _2F_1\left(-\frac{3}{2},\frac{1}{4} \left(-3-\frac{2 i}{b n}\right);\frac{1}{4} \left(1-\frac{2 i}{b n}\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2-3 i b n) \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \csc ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}",1,"(2*x*Hypergeometric2F1[-3/2, (-3 - (2*I)/(b*n))/4, (1 - (2*I)/(b*n))/4, E^((2*I)*a)*(c*x^n)^((2*I)*b)])/((2 - (3*I)*b*n)*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^(3/2)*Csc[a + b*Log[c*x^n]]^(3/2))","A",3,3,15,0.2000,1,"{4504, 4508, 364}"
317,1,98,0,0.0589235,"\int \frac{1}{x \csc ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[1/(x*Csc[a + b*Log[c*x^n]]^(3/2)),x]","\frac{2 \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)} \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{3 b n}-\frac{2 \cos \left(a+b \log \left(c x^n\right)\right)}{3 b n \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)}}","\frac{2 \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)} \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{3 b n}-\frac{2 \cos \left(a+b \log \left(c x^n\right)\right)}{3 b n \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)}}",1,"(-2*Cos[a + b*Log[c*x^n]])/(3*b*n*Sqrt[Csc[a + b*Log[c*x^n]]]) + (2*Sqrt[Csc[a + b*Log[c*x^n]]]*EllipticF[(a - Pi/2 + b*Log[c*x^n])/2, 2]*Sqrt[Sin[a + b*Log[c*x^n]]])/(3*b*n)","A",4,3,19,0.1579,1,"{3769, 3771, 2641}"
318,1,110,0,0.0731525,"\int \frac{1}{\csc ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[Csc[a + b*Log[c*x^n]]^(-5/2),x]","\frac{2 x \, _2F_1\left(-\frac{5}{2},\frac{1}{4} \left(-5-\frac{2 i}{b n}\right);-\frac{b n+2 i}{4 b n};e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2-5 i b n) \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2} \csc ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}","\frac{2 x \, _2F_1\left(-\frac{5}{2},\frac{1}{4} \left(-5-\frac{2 i}{b n}\right);-\frac{b n+2 i}{4 b n};e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(2-5 i b n) \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2} \csc ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}",1,"(2*x*Hypergeometric2F1[-5/2, (-5 - (2*I)/(b*n))/4, -(2*I + b*n)/(4*b*n), E^((2*I)*a)*(c*x^n)^((2*I)*b)])/((2 - (5*I)*b*n)*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^(5/2)*Csc[a + b*Log[c*x^n]]^(5/2))","A",3,3,15,0.2000,1,"{4504, 4508, 364}"
319,1,98,0,0.0583067,"\int \frac{1}{x \csc ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[1/(x*Csc[a + b*Log[c*x^n]]^(5/2)),x]","\frac{6 \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)} \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{5 b n}-\frac{2 \cos \left(a+b \log \left(c x^n\right)\right)}{5 b n \csc ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}","\frac{6 \sqrt{\sin \left(a+b \log \left(c x^n\right)\right)} \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} \left(a+b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{5 b n}-\frac{2 \cos \left(a+b \log \left(c x^n\right)\right)}{5 b n \csc ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}",1,"(-2*Cos[a + b*Log[c*x^n]])/(5*b*n*Csc[a + b*Log[c*x^n]]^(3/2)) + (6*Sqrt[Csc[a + b*Log[c*x^n]]]*EllipticE[(a - Pi/2 + b*Log[c*x^n])/2, 2]*Sqrt[Sin[a + b*Log[c*x^n]]])/(5*b*n)","A",4,3,19,0.1579,1,"{3769, 3771, 2639}"
320,1,122,0,0.1096169,"\int (e x)^m \csc ^3\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Csc[d*(a + b*Log[c*x^n])]^3,x]","-\frac{8 e^{3 i a d} (e x)^{m+1} \left(c x^n\right)^{3 i b d} \, _2F_1\left(3,-\frac{i (m+1)-3 b d n}{2 b d n};-\frac{i (m+1)-5 b d n}{2 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{e (-3 b d n+i (m+1))}","-\frac{8 e^{3 i a d} (e x)^{m+1} \left(c x^n\right)^{3 i b d} \, _2F_1\left(3,-\frac{i (m+1)-3 b d n}{2 b d n};-\frac{i (m+1)-5 b d n}{2 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{e (-3 b d n+i (m+1))}",1,"(-8*E^((3*I)*a*d)*(e*x)^(1 + m)*(c*x^n)^((3*I)*b*d)*Hypergeometric2F1[3, -(I*(1 + m) - 3*b*d*n)/(2*b*d*n), -(I*(1 + m) - 5*b*d*n)/(2*b*d*n), E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d)])/(e*(I*(1 + m) - 3*b*d*n))","A",3,3,21,0.1429,1,"{4510, 4506, 364}"
321,1,119,0,0.0966439,"\int (e x)^m \csc ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Csc[d*(a + b*Log[c*x^n])]^2,x]","-\frac{4 e^{2 i a d} (e x)^{m+1} \left(c x^n\right)^{2 i b d} \, _2F_1\left(2,-\frac{i (m+1)-2 b d n}{2 b d n};-\frac{i (m+1)-4 b d n}{2 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{e (2 i b d n+m+1)}","-\frac{4 e^{2 i a d} (e x)^{m+1} \left(c x^n\right)^{2 i b d} \, _2F_1\left(2,-\frac{i (m+1)-2 b d n}{2 b d n};-\frac{i (m+1)-4 b d n}{2 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{e (2 i b d n+m+1)}",1,"(-4*E^((2*I)*a*d)*(e*x)^(1 + m)*(c*x^n)^((2*I)*b*d)*Hypergeometric2F1[2, -(I*(1 + m) - 2*b*d*n)/(2*b*d*n), -(I*(1 + m) - 4*b*d*n)/(2*b*d*n), E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d)])/(e*(1 + m + (2*I)*b*d*n))","A",3,3,21,0.1429,1,"{4510, 4506, 364}"
322,1,118,0,0.0770617,"\int (e x)^m \csc \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Csc[d*(a + b*Log[c*x^n])],x]","\frac{2 e^{i a d} (e x)^{m+1} \left(c x^n\right)^{i b d} \, _2F_1\left(1,\frac{1}{2} \left(1-\frac{i (m+1)}{b d n}\right);-\frac{i (m+1)-3 b d n}{2 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{e (-b d n+i (m+1))}","\frac{2 e^{i a d} (e x)^{m+1} \left(c x^n\right)^{i b d} \, _2F_1\left(1,-\frac{i m-b d n+i}{2 b d n};-\frac{i (m+1)-3 b d n}{2 b d n};e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)}{e (-b d n+i (m+1))}",1,"(2*E^(I*a*d)*(e*x)^(1 + m)*(c*x^n)^(I*b*d)*Hypergeometric2F1[1, (1 - (I*(1 + m))/(b*d*n))/2, -(I*(1 + m) - 3*b*d*n)/(2*b*d*n), E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d)])/(e*(I*(1 + m) - b*d*n))","A",3,3,19,0.1579,1,"{4510, 4506, 364}"
323,1,126,0,0.0961908,"\int x^m \csc ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^m*Csc[a + b*Log[c*x^n]]^(5/2),x]","\frac{2 x^{m+1} \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2} \, _2F_1\left(\frac{5}{2},\frac{1}{4} \left(5-\frac{2 i (m+1)}{b n}\right);-\frac{2 i m-9 b n+2 i}{4 b n};e^{2 i a} \left(c x^n\right)^{2 i b}\right) \csc ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{5 i b n+2 m+2}","\frac{2 x^{m+1} \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{5/2} \, _2F_1\left(\frac{5}{2},-\frac{2 i m-5 b n+2 i}{4 b n};-\frac{2 i m-9 b n+2 i}{4 b n};e^{2 i a} \left(c x^n\right)^{2 i b}\right) \csc ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{5 i b n+2 m+2}",1,"(2*x^(1 + m)*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^(5/2)*Csc[a + b*Log[c*x^n]]^(5/2)*Hypergeometric2F1[5/2, (5 - ((2*I)*(1 + m))/(b*n))/4, -(2*I + (2*I)*m - 9*b*n)/(4*b*n), E^((2*I)*a)*(c*x^n)^((2*I)*b)])/(2 + 2*m + (5*I)*b*n)","A",3,3,19,0.1579,1,"{4510, 4508, 364}"
324,1,126,0,0.09169,"\int x^m \csc ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^m*Csc[a + b*Log[c*x^n]]^(3/2),x]","\frac{2 x^{m+1} \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{1}{4} \left(3-\frac{2 i (m+1)}{b n}\right);-\frac{2 i m-7 b n+2 i}{4 b n};e^{2 i a} \left(c x^n\right)^{2 i b}\right) \csc ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{3 i b n+2 m+2}","\frac{2 x^{m+1} \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \, _2F_1\left(\frac{3}{2},-\frac{2 i m-3 b n+2 i}{4 b n};-\frac{2 i m-7 b n+2 i}{4 b n};e^{2 i a} \left(c x^n\right)^{2 i b}\right) \csc ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{3 i b n+2 m+2}",1,"(2*x^(1 + m)*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^(3/2)*Csc[a + b*Log[c*x^n]]^(3/2)*Hypergeometric2F1[3/2, (3 - ((2*I)*(1 + m))/(b*n))/4, -(2*I + (2*I)*m - 7*b*n)/(4*b*n), E^((2*I)*a)*(c*x^n)^((2*I)*b)])/(2 + 2*m + (3*I)*b*n)","A",3,3,19,0.1579,1,"{4510, 4508, 364}"
325,1,130,0,0.0924365,"\int x^m \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)} \, dx","Int[x^m*Sqrt[Csc[a + b*Log[c*x^n]]],x]","\frac{2 x^{m+1} \sqrt{1-e^{2 i a} \left(c x^n\right)^{2 i b}} \, _2F_1\left(\frac{1}{2},-\frac{2 i m-b n+2 i}{4 b n};-\frac{2 i m-5 b n+2 i}{4 b n};e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)}}{i b n+2 m+2}","\frac{2 x^{m+1} \sqrt{1-e^{2 i a} \left(c x^n\right)^{2 i b}} \, _2F_1\left(\frac{1}{2},-\frac{2 i m-b n+2 i}{4 b n};-\frac{2 i m-5 b n+2 i}{4 b n};e^{2 i a} \left(c x^n\right)^{2 i b}\right) \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)}}{i b n+2 m+2}",1,"(2*x^(1 + m)*Sqrt[1 - E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Sqrt[Csc[a + b*Log[c*x^n]]]*Hypergeometric2F1[1/2, -(2*I + (2*I)*m - b*n)/(4*b*n), -(2*I + (2*I)*m - 5*b*n)/(4*b*n), E^((2*I)*a)*(c*x^n)^((2*I)*b)])/(2 + 2*m + I*b*n)","A",3,3,19,0.1579,1,"{4510, 4508, 364}"
326,1,126,0,0.0883437,"\int \frac{x^m}{\sqrt{\csc \left(a+b \log \left(c x^n\right)\right)}} \, dx","Int[x^m/Sqrt[Csc[a + b*Log[c*x^n]]],x]","\frac{2 x^{m+1} \, _2F_1\left(-\frac{1}{2},\frac{1}{4} \left(-\frac{2 i (m+1)}{b n}-1\right);-\frac{2 i m-3 b n+2 i}{4 b n};e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(-i b n+2 m+2) \sqrt{1-e^{2 i a} \left(c x^n\right)^{2 i b}} \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)}}","\frac{2 x^{m+1} \, _2F_1\left(-\frac{1}{2},-\frac{2 i m+b n+2 i}{4 b n};-\frac{2 i m-3 b n+2 i}{4 b n};e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(-i b n+2 m+2) \sqrt{1-e^{2 i a} \left(c x^n\right)^{2 i b}} \sqrt{\csc \left(a+b \log \left(c x^n\right)\right)}}",1,"(2*x^(1 + m)*Hypergeometric2F1[-1/2, (-1 - ((2*I)*(1 + m))/(b*n))/4, -(2*I + (2*I)*m - 3*b*n)/(4*b*n), E^((2*I)*a)*(c*x^n)^((2*I)*b)])/((2 + 2*m - I*b*n)*Sqrt[1 - E^((2*I)*a)*(c*x^n)^((2*I)*b)]*Sqrt[Csc[a + b*Log[c*x^n]]])","A",3,3,19,0.1579,1,"{4510, 4508, 364}"
327,1,126,0,0.0943862,"\int \frac{x^m}{\csc ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[x^m/Csc[a + b*Log[c*x^n]]^(3/2),x]","\frac{2 x^{m+1} \, _2F_1\left(-\frac{3}{2},\frac{1}{4} \left(-\frac{2 i (m+1)}{b n}-3\right);-\frac{2 i m-b n+2 i}{4 b n};e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(-3 i b n+2 m+2) \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \csc ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}","\frac{2 x^{m+1} \, _2F_1\left(-\frac{3}{2},-\frac{2 i m+3 b n+2 i}{4 b n};-\frac{2 i m-b n+2 i}{4 b n};e^{2 i a} \left(c x^n\right)^{2 i b}\right)}{(-3 i b n+2 m+2) \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^{3/2} \csc ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}",1,"(2*x^(1 + m)*Hypergeometric2F1[-3/2, (-3 - ((2*I)*(1 + m))/(b*n))/4, -(2*I + (2*I)*m - b*n)/(4*b*n), E^((2*I)*a)*(c*x^n)^((2*I)*b)])/((2 + 2*m - (3*I)*b*n)*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^(3/2)*Csc[a + b*Log[c*x^n]]^(3/2))","A",3,3,19,0.1579,1,"{4510, 4508, 364}"
328,1,133,0,0.1131121,"\int (e x)^m \csc ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Csc[d*(a + b*Log[c*x^n])]^p,x]","\frac{(e x)^{m+1} \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^p \, _2F_1\left(p,\frac{1}{2} \left(p-\frac{i (m+1)}{b d n}\right);\frac{1}{2} \left(-\frac{i (m+1)}{b d n}+p+2\right);e^{2 i a d} \left(c x^n\right)^{2 i b d}\right) \csc ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e (i b d n p+m+1)}","\frac{(e x)^{m+1} \left(1-e^{2 i a d} \left(c x^n\right)^{2 i b d}\right)^p \, _2F_1\left(p,-\frac{i m-b d n p+i}{2 b d n};\frac{1}{2} \left(-\frac{i (m+1)}{b d n}+p+2\right);e^{2 i a d} \left(c x^n\right)^{2 i b d}\right) \csc ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e (i b d n p+m+1)}",1,"((e*x)^(1 + m)*(1 - E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d))^p*Csc[d*(a + b*Log[c*x^n])]^p*Hypergeometric2F1[p, (((-I)*(1 + m))/(b*d*n) + p)/2, (2 - (I*(1 + m))/(b*d*n) + p)/2, E^((2*I)*a*d)*(c*x^n)^((2*I)*b*d)])/(e*(1 + m + I*b*d*n*p))","A",3,3,21,0.1429,1,"{4510, 4508, 364}"
329,1,106,0,0.0755096,"\int x \csc ^p\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Csc[a + b*Log[c*x^n]]^p,x]","\frac{x^2 \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^p \, _2F_1\left(p,\frac{1}{2} \left(p-\frac{2 i}{b n}\right);\frac{1}{2} \left(p-\frac{2 i}{b n}+2\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \csc ^p\left(a+b \log \left(c x^n\right)\right)}{2+i b n p}","\frac{x^2 \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^p \, _2F_1\left(p,\frac{1}{2} \left(p-\frac{2 i}{b n}\right);\frac{1}{2} \left(p-\frac{2 i}{b n}+2\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \csc ^p\left(a+b \log \left(c x^n\right)\right)}{2+i b n p}",1,"(x^2*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^p*Csc[a + b*Log[c*x^n]]^p*Hypergeometric2F1[p, ((-2*I)/(b*n) + p)/2, (2 - (2*I)/(b*n) + p)/2, E^((2*I)*a)*(c*x^n)^((2*I)*b)])/(2 + I*b*n*p)","A",3,3,15,0.2000,1,"{4510, 4508, 364}"
330,1,107,0,0.0664191,"\int \csc ^p\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Csc[a + b*Log[c*x^n]]^p,x]","\frac{x \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^p \, _2F_1\left(p,-\frac{i-b n p}{2 b n};\frac{1}{2} \left(p-\frac{i}{b n}+2\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \csc ^p\left(a+b \log \left(c x^n\right)\right)}{1+i b n p}","\frac{x \left(1-e^{2 i a} \left(c x^n\right)^{2 i b}\right)^p \, _2F_1\left(p,-\frac{i-b n p}{2 b n};\frac{1}{2} \left(p-\frac{i}{b n}+2\right);e^{2 i a} \left(c x^n\right)^{2 i b}\right) \csc ^p\left(a+b \log \left(c x^n\right)\right)}{1+i b n p}",1,"(x*(1 - E^((2*I)*a)*(c*x^n)^((2*I)*b))^p*Csc[a + b*Log[c*x^n]]^p*Hypergeometric2F1[p, -(I - b*n*p)/(2*b*n), (2 - I/(b*n) + p)/2, E^((2*I)*a)*(c*x^n)^((2*I)*b)])/(1 + I*b*n*p)","A",3,3,13,0.2308,1,"{4504, 4508, 364}"