1,0,0,75,0.852000," ","int(ln(c*x^n)^(-1+q)*(a*x^m+b*ln(c*x^n)^q)^p/x,x)","\int \frac{\left(a \,x^{m}+b \ln \left(c \,x^{n}\right)^{q}\right)^{p} \ln \left(c \,x^{n}\right)^{q -1}}{x}\, dx"," ",0,"int(ln(c*x^n)^(-1+q)*(a*x^m+b*ln(c*x^n)^q)^p/x,x)","F"
2,0,0,238,20.380000," ","int(ln(c*x^n)^(q-1)*(a*x^m+b*ln(c*x^n)^q)^3/x,x)","\int \frac{\left(a \,x^{m}+b \ln \left(c \,x^{n}\right)^{q}\right)^{3} \ln \left(c \,x^{n}\right)^{q -1}}{x}\, dx"," ",0,"int(ln(c*x^n)^(q-1)*(a*x^m+b*ln(c*x^n)^q)^3/x,x)","F"
3,0,0,159,13.005000," ","int(ln(c*x^n)^(q-1)*(a*x^m+b*ln(c*x^n)^q)^2/x,x)","\int \frac{\left(a \,x^{m}+b \ln \left(c \,x^{n}\right)^{q}\right)^{2} \ln \left(c \,x^{n}\right)^{q -1}}{x}\, dx"," ",0,"int(ln(c*x^n)^(q-1)*(a*x^m+b*ln(c*x^n)^q)^2/x,x)","F"
4,0,0,80,21.042000," ","int(ln(c*x^n)^(q-1)*(a*x^m+b*ln(c*x^n)^q)/x,x)","\int \frac{\left(a \,x^{m}+b \ln \left(c \,x^{n}\right)^{q}\right) \ln \left(c \,x^{n}\right)^{q -1}}{x}\, dx"," ",0,"int(ln(c*x^n)^(q-1)*(a*x^m+b*ln(c*x^n)^q)/x,x)","F"
5,1,16,15,0.065000," ","int(ln(c*x^n)^(q-1)/x,x)","\frac{\ln \left(c \,x^{n}\right)^{q}}{n q}"," ",0,"ln(c*x^n)^q/n/q","A"
6,0,0,67,29.522000," ","int(ln(c*x^n)^(q-1)/x/(a*x^m+b*ln(c*x^n)^q),x)","\int \frac{\ln \left(c \,x^{n}\right)^{q -1}}{\left(a \,x^{m}+b \ln \left(c \,x^{n}\right)^{q}\right) x}\, dx"," ",0,"int(ln(c*x^n)^(q-1)/x/(a*x^m+b*ln(c*x^n)^q),x)","F"
7,0,0,69,50.166000," ","int(ln(c*x^n)^(q-1)/x/(a*x^m+b*ln(c*x^n)^q)^2,x)","\int \frac{\ln \left(c \,x^{n}\right)^{q -1}}{\left(a \,x^{m}+b \ln \left(c \,x^{n}\right)^{q}\right)^{2} x}\, dx"," ",0,"int(ln(c*x^n)^(q-1)/x/(a*x^m+b*ln(c*x^n)^q)^2,x)","F"
8,0,0,69,121.280000," ","int(ln(c*x^n)^(q-1)/x/(a*x^m+b*ln(c*x^n)^q)^3,x)","\int \frac{\ln \left(c \,x^{n}\right)^{q -1}}{\left(a \,x^{m}+b \ln \left(c \,x^{n}\right)^{q}\right)^{3} x}\, dx"," ",0,"int(ln(c*x^n)^(q-1)/x/(a*x^m+b*ln(c*x^n)^q)^3,x)","F"
9,1,61910,258,9.064000," ","int(ln(c*x^n)*(a*x^m+b*ln(c*x^n)^2)^3/x,x)","\text{output too large to display}"," ",0,"result too large to display","C"
10,1,14983,119,3.162000," ","int(ln(c*x^n)*(a*x^m+b*ln(c*x^n)^2)^2/x,x)","\text{output too large to display}"," ",0,"result too large to display","C"
11,1,2146,39,1.047000," ","int(ln(c*x^n)*(a*x^m+b*ln(c*x^n)^2)/x,x)","\text{Expression too large to display}"," ",0,"1/4*(-3*Pi^2*b*csgn(I*x^n)^2*csgn(I*c*x^n)^4*ln(x)*m+6*Pi^2*b*csgn(I*x^n)^2*csgn(I*c*x^n)^3*csgn(I*c)*ln(x)*m-3*Pi^2*b*csgn(I*x^n)^2*csgn(I*c*x^n)^2*csgn(I*c)^2*ln(x)*m+6*Pi^2*b*csgn(I*x^n)*csgn(I*c*x^n)^5*ln(x)*m-12*Pi^2*b*csgn(I*x^n)*csgn(I*c*x^n)^4*csgn(I*c)*ln(x)*m+6*Pi^2*b*csgn(I*x^n)*csgn(I*c*x^n)^3*csgn(I*c)^2*ln(x)*m-3*Pi^2*b*csgn(I*c*x^n)^6*ln(x)*m+6*Pi^2*b*csgn(I*c*x^n)^5*csgn(I*c)*ln(x)*m-3*Pi^2*b*csgn(I*c*x^n)^4*csgn(I*c)^2*ln(x)*m+6*I*ln(x)^2*Pi*b*n*csgn(I*c*x^n)^3*m+6*I*ln(x)^2*Pi*b*n*csgn(I*x^n)*csgn(I*c*x^n)*csgn(I*c)*m-6*I*ln(x)^2*Pi*b*n*csgn(I*x^n)*csgn(I*c*x^n)^2*m+12*I*ln(c)*Pi*b*csgn(I*x^n)*csgn(I*c*x^n)^2*ln(x)*m-12*I*ln(c)*Pi*b*csgn(I*x^n)*csgn(I*c*x^n)*csgn(I*c)*ln(x)*m+12*I*ln(c)*Pi*b*csgn(I*c*x^n)^2*csgn(I*c)*ln(x)*m-6*I*ln(x)^2*Pi*b*n*csgn(I*c*x^n)^2*csgn(I*c)*m-12*I*ln(c)*Pi*b*csgn(I*c*x^n)^3*ln(x)*m+4*b*n^2*ln(x)^3*m-12*ln(x)^2*ln(c)*b*n*m+12*ln(c)^2*b*ln(x)*m+4*a*x^m)/m*ln(x^n)+b*ln(x)*ln(x^n)^3+ln(c)^3*ln(x)*b-1/4*b*n^3*ln(x)^4-a*n*x^m/m^2+1/m*ln(c)*a*x^m+ln(x)^3*ln(c)*b*n^2-3/2*ln(x)^2*ln(c)^2*b*n-3/4*csgn(I*c)*csgn(I*c*x^n)^5*n*b*Pi^2*ln(x)^2+3/8*csgn(I*c)^2*csgn(I*c*x^n)^4*n*b*Pi^2*ln(x)^2-3/4*ln(x)*csgn(I*c*x^n)^4*csgn(I*x^n)^2*b*Pi^2*ln(c)+3/2*ln(x)*csgn(I*c*x^n)^5*csgn(I*x^n)*b*Pi^2*ln(c)+3/2*ln(x)*csgn(I*c)*csgn(I*c*x^n)^5*b*Pi^2*ln(c)-3/4*ln(x)*csgn(I*c)^2*csgn(I*c*x^n)^4*b*Pi^2*ln(c)-3/4*ln(x)*csgn(I*c*x^n)^6*b*Pi^2*ln(c)+3/8*csgn(I*c*x^n)^6*n*b*Pi^2*ln(x)^2+3/2*I*ln(x)^2*ln(c)*Pi*b*n*csgn(I*x^n)*csgn(I*c*x^n)*csgn(I*c)-3/8*I*Pi^3*b*csgn(I*c*x^n)^8*csgn(I*c)*ln(x)-3/8*I*Pi^3*b*csgn(I*x^n)*csgn(I*c*x^n)^8*ln(x)+3/8*I*Pi^3*b*csgn(I*c*x^n)^7*csgn(I*c)^2*ln(x)+3/8*I*Pi^3*b*csgn(I*x^n)^2*csgn(I*c*x^n)^7*ln(x)-1/8*I*Pi^3*b*csgn(I*c*x^n)^6*csgn(I*c)^3*ln(x)-1/8*I*Pi^3*b*csgn(I*x^n)^3*csgn(I*c*x^n)^6*ln(x)-1/2*I*ln(x)^3*Pi*b*n^2*csgn(I*c*x^n)^3-3/2*I*ln(c)^2*Pi*b*csgn(I*c*x^n)^3*ln(x)-1/2*I/m*Pi*a*csgn(I*c*x^n)^3*x^m+3/8*csgn(I*c*x^n)^4*csgn(I*x^n)^2*n*b*Pi^2*ln(x)^2-3/4*csgn(I*c*x^n)^5*csgn(I*x^n)*n*b*Pi^2*ln(x)^2-3*ln(x)*csgn(I*c)*csgn(I*c*x^n)^4*csgn(I*x^n)*b*Pi^2*ln(c)+3/2*ln(x)*csgn(I*c)^2*csgn(I*c*x^n)^3*csgn(I*x^n)*b*Pi^2*ln(c)+3/8*csgn(I*c)^2*csgn(I*c*x^n)^2*csgn(I*x^n)^2*n*b*Pi^2*ln(x)^2+3/2*csgn(I*c)*csgn(I*c*x^n)^4*csgn(I*x^n)*n*b*Pi^2*ln(x)^2-3/4*csgn(I*c)^2*csgn(I*c*x^n)^3*csgn(I*x^n)*n*b*Pi^2*ln(x)^2+3/2*ln(x)*csgn(I*c)*csgn(I*c*x^n)^3*csgn(I*x^n)^2*b*Pi^2*ln(c)-3/4*ln(x)*csgn(I*c)^2*csgn(I*c*x^n)^2*csgn(I*x^n)^2*b*Pi^2*ln(c)-3/4*csgn(I*c)*csgn(I*c*x^n)^3*csgn(I*x^n)^2*n*b*Pi^2*ln(x)^2+1/8*I*ln(x)*csgn(I*c*x^n)^9*b*Pi^3-3/2*I*ln(x)^2*ln(c)*Pi*b*n*csgn(I*c*x^n)^2*csgn(I*c)+1/2*I/m*Pi*a*csgn(I*c*x^n)^2*csgn(I*c)*x^m+1/2*I/m*Pi*a*csgn(I*x^n)*csgn(I*c*x^n)^2*x^m+9/8*I*Pi^3*b*csgn(I*x^n)*csgn(I*c*x^n)^7*csgn(I*c)*ln(x)-9/8*I*Pi^3*b*csgn(I*x^n)*csgn(I*c*x^n)^6*csgn(I*c)^2*ln(x)-9/8*I*Pi^3*b*csgn(I*x^n)^2*csgn(I*c*x^n)^6*csgn(I*c)*ln(x)+3/8*I*Pi^3*b*csgn(I*x^n)*csgn(I*c*x^n)^5*csgn(I*c)^3*ln(x)+9/8*I*Pi^3*b*csgn(I*x^n)^2*csgn(I*c*x^n)^5*csgn(I*c)^2*ln(x)+3/8*I*Pi^3*b*csgn(I*x^n)^3*csgn(I*c*x^n)^5*csgn(I*c)*ln(x)-3/8*I*Pi^3*b*csgn(I*x^n)^2*csgn(I*c*x^n)^4*csgn(I*c)^3*ln(x)-3/8*I*Pi^3*b*csgn(I*x^n)^3*csgn(I*c*x^n)^4*csgn(I*c)^2*ln(x)+1/8*I*ln(x)*csgn(I*c)^3*csgn(I*c*x^n)^3*csgn(I*x^n)^3*b*Pi^3+1/2*I*ln(x)^3*Pi*b*n^2*csgn(I*c*x^n)^2*csgn(I*c)+1/2*I*ln(x)^3*Pi*b*n^2*csgn(I*x^n)*csgn(I*c*x^n)^2+3/2*I*ln(x)^2*ln(c)*Pi*b*n*csgn(I*c*x^n)^3+3/2*I*ln(c)^2*Pi*b*csgn(I*c*x^n)^2*csgn(I*c)*ln(x)+3/2*I*ln(c)^2*Pi*b*csgn(I*x^n)*csgn(I*c*x^n)^2*ln(x)+(-3/2*b*n*ln(x)^2+3/2*I*Pi*b*csgn(I*x^n)*csgn(I*c*x^n)^2*ln(x)-3/2*I*Pi*b*csgn(I*x^n)*csgn(I*c*x^n)*csgn(I*c)*ln(x)-3/2*I*Pi*b*csgn(I*c*x^n)^3*ln(x)+3/2*I*Pi*b*csgn(I*c*x^n)^2*csgn(I*c)*ln(x)+3*b*ln(c)*ln(x))*ln(x^n)^2-3/2*I*ln(x)^2*ln(c)*Pi*b*n*csgn(I*x^n)*csgn(I*c*x^n)^2-3/2*I*ln(c)^2*Pi*b*csgn(I*x^n)*csgn(I*c*x^n)*csgn(I*c)*ln(x)-1/2*I*ln(x)^3*Pi*b*n^2*csgn(I*x^n)*csgn(I*c*x^n)*csgn(I*c)-1/2*I/m*Pi*a*csgn(I*x^n)*csgn(I*c*x^n)*csgn(I*c)*x^m","C"
12,1,14,13,0.066000," ","int(ln(c*x^n)/x,x)","\frac{\ln \left(c \,x^{n}\right)^{2}}{2 n}"," ",0,"1/2*ln(c*x^n)^2/n","A"
13,0,0,62,7.099000," ","int(ln(c*x^n)/x/(a*x^m+b*ln(c*x^n)^2),x)","\int \frac{\ln \left(c \,x^{n}\right)}{\left(b \ln \left(c \,x^{n}\right)^{2}+a \,x^{m}\right) x}\, dx"," ",0,"int(ln(c*x^n)/x/(a*x^m+b*ln(c*x^n)^2),x)","F"
14,0,0,63,107.741000," ","int(ln(c*x^n)/x/(b*ln(c*x^n)^2+a*x^m)^2,x)","\int \frac{\ln \left(c \,x^{n}\right)}{\left(b \ln \left(c \,x^{n}\right)^{2}+a \,x^{m}\right)^{2} x}\, dx"," ",0,"int(ln(c*x^n)/x/(b*ln(c*x^n)^2+a*x^m)^2,x)","F"
15,0,0,63,127.671000," ","int(ln(c*x^n)/x/(b*ln(c*x^n)^2+a*x^m)^3,x)","\int \frac{\ln \left(c \,x^{n}\right)}{\left(b \ln \left(c \,x^{n}\right)^{2}+a \,x^{m}\right)^{3} x}\, dx"," ",0,"int(ln(c*x^n)/x/(b*ln(c*x^n)^2+a*x^m)^3,x)","F"
16,0,0,26,0.967000," ","int((a*m*x^m+b*n*q*ln(c*x^n)^(q-1))*(a*x^m+b*ln(c*x^n)^q)^p/x,x)","\int \frac{\left(b n q \ln \left(c \,x^{n}\right)^{q -1}+a m \,x^{m}\right) \left(a \,x^{m}+b \ln \left(c \,x^{n}\right)^{q}\right)^{p}}{x}\, dx"," ",0,"int((a*m*x^m+b*n*q*ln(c*x^n)^(q-1))*(a*x^m+b*ln(c*x^n)^q)^p/x,x)","F"
17,1,204,20,0.662000," ","int((b*n*q*ln(c*x^n)^(q-1)+a*m*x^m)*(a*x^m+b*ln(c*x^n)^q)^2/x,x)","a^{2} b \,x^{2 m} \left(-\frac{i \pi  \left(\mathrm{csgn}\left(i c \right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \left(\mathrm{csgn}\left(i x^{n}\right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \mathrm{csgn}\left(i c \,x^{n}\right)}{2}+\ln \left(c \right)+\ln \left(x^{n}\right)\right)^{q}+a \,b^{2} x^{m} \left(-\frac{i \pi  \left(\mathrm{csgn}\left(i c \right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \left(\mathrm{csgn}\left(i x^{n}\right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \mathrm{csgn}\left(i c \,x^{n}\right)}{2}+\ln \left(c \right)+\ln \left(x^{n}\right)\right)^{2 q}+\frac{a^{3} x^{3 m}}{3}+\frac{b^{3} \left(-\frac{i \pi  \left(\mathrm{csgn}\left(i c \right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \left(\mathrm{csgn}\left(i x^{n}\right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \mathrm{csgn}\left(i c \,x^{n}\right)}{2}+\ln \left(c \right)+\ln \left(x^{n}\right)\right)^{3 q}}{3}"," ",0,"1/3*a^3*(x^m)^3+1/3*b^3*((ln(c)+ln(x^n)-1/2*I*Pi*csgn(I*c*x^n)*(-csgn(I*c*x^n)+csgn(I*c))*(-csgn(I*c*x^n)+csgn(I*x^n)))^q)^3+a*b^2*x^m*((ln(c)+ln(x^n)-1/2*I*Pi*csgn(I*c*x^n)*(-csgn(I*c*x^n)+csgn(I*c))*(-csgn(I*c*x^n)+csgn(I*x^n)))^q)^2+a^2*b*(x^m)^2*(ln(c)+ln(x^n)-1/2*I*Pi*csgn(I*c*x^n)*(-csgn(I*c*x^n)+csgn(I*c))*(-csgn(I*c*x^n)+csgn(I*x^n)))^q","C"
18,1,135,20,0.674000," ","int((b*n*q*ln(c*x^n)^(q-1)+a*m*x^m)*(a*x^m+b*ln(c*x^n)^q)/x,x)","a b \,x^{m} \left(-\frac{i \pi  \left(\mathrm{csgn}\left(i c \right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \left(\mathrm{csgn}\left(i x^{n}\right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \mathrm{csgn}\left(i c \,x^{n}\right)}{2}+\ln \left(c \right)+\ln \left(x^{n}\right)\right)^{q}+\frac{a^{2} x^{2 m}}{2}+\frac{b^{2} \left(-\frac{i \pi  \left(\mathrm{csgn}\left(i c \right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \left(\mathrm{csgn}\left(i x^{n}\right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \mathrm{csgn}\left(i c \,x^{n}\right)}{2}+\ln \left(c \right)+\ln \left(x^{n}\right)\right)^{2 q}}{2}"," ",0,"1/2*a^2*(x^m)^2+1/2*b^2*((-1/2*I*Pi*(csgn(I*c)-csgn(I*c*x^n))*(csgn(I*x^n)-csgn(I*c*x^n))*csgn(I*c*x^n)+ln(c)+ln(x^n))^q)^2+a*b*x^m*(-1/2*I*Pi*(csgn(I*c)-csgn(I*c*x^n))*(csgn(I*x^n)-csgn(I*c*x^n))*csgn(I*c*x^n)+ln(c)+ln(x^n))^q","C"
19,1,17,16,0.078000," ","int((b*n*q*ln(c*x^n)^(q-1)+a*m*x^m)/x,x)","a \,x^{m}+b \ln \left(c \,x^{n}\right)^{q}"," ",0,"a*x^m+b*ln(c*x^n)^q","A"
20,1,212,17,0.583000," ","int((b*n*q*ln(c*x^n)^(q-1)+a*m*x^m)/x/(a*x^m+b*ln(c*x^n)^q),x)","-q \ln \left(-\frac{i \pi  \left(\mathrm{csgn}\left(i c \right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \left(\mathrm{csgn}\left(i x^{n}\right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \mathrm{csgn}\left(i c \,x^{n}\right)}{2}+\ln \left(c \right)+\ln \left(x^{n}\right)\right)+q \ln \left(-\frac{i \pi  \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)}{2}+\frac{i \pi  \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i c \,x^{n}\right)^{2}}{2}+\frac{i \pi  \,\mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)^{2}}{2}-\frac{i \pi  \mathrm{csgn}\left(i c \,x^{n}\right)^{3}}{2}+\ln \left(c \right)+\ln \left(x^{n}\right)\right)+\ln \left(\frac{a \,x^{m}}{b}+\left(-\frac{i \pi  \left(\mathrm{csgn}\left(i c \right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \left(\mathrm{csgn}\left(i x^{n}\right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \mathrm{csgn}\left(i c \,x^{n}\right)}{2}+\ln \left(c \right)+\ln \left(x^{n}\right)\right)^{q}\right)"," ",0,"q*ln(ln(c)+ln(x^n)-1/2*I*Pi*csgn(I*c*x^n)^3+1/2*I*Pi*csgn(I*c*x^n)^2*csgn(I*c)+1/2*I*Pi*csgn(I*x^n)*csgn(I*c*x^n)^2-1/2*I*Pi*csgn(I*c*x^n)*csgn(I*c)*csgn(I*x^n))-q*ln(-1/2*I*Pi*(csgn(I*c)-csgn(I*c*x^n))*(csgn(I*x^n)-csgn(I*c*x^n))*csgn(I*c*x^n)+ln(c)+ln(x^n))+ln((-1/2*I*Pi*(csgn(I*c)-csgn(I*c*x^n))*(csgn(I*x^n)-csgn(I*c*x^n))*csgn(I*c*x^n)+ln(c)+ln(x^n))^q+1/b*a*x^m)","C"
21,1,68,20,0.538000," ","int((b*n*q*ln(c*x^n)^(q-1)+a*m*x^m)/x/(a*x^m+b*ln(c*x^n)^q)^2,x)","-\frac{1}{a \,x^{m}+b \left(-\frac{i \pi  \left(\mathrm{csgn}\left(i c \right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \left(\mathrm{csgn}\left(i x^{n}\right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \mathrm{csgn}\left(i c \,x^{n}\right)}{2}+\ln \left(c \right)+\ln \left(x^{n}\right)\right)^{q}}"," ",0,"-1/(a*x^m+b*(-1/2*I*Pi*(csgn(I*c)-csgn(I*c*x^n))*(csgn(I*x^n)-csgn(I*c*x^n))*csgn(I*c*x^n)+ln(c)+ln(x^n))^q)","C"
22,1,68,20,5.440000," ","int((b*n*q*ln(c*x^n)^(q-1)+a*m*x^m)/x/(a*x^m+b*ln(c*x^n)^q)^3,x)","-\frac{1}{2 \left(a \,x^{m}+b \left(-\frac{i \pi  \left(\mathrm{csgn}\left(i c \right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \left(\mathrm{csgn}\left(i x^{n}\right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \mathrm{csgn}\left(i c \,x^{n}\right)}{2}+\ln \left(c \right)+\ln \left(x^{n}\right)\right)^{q}\right)^{2}}"," ",0,"-1/2/(a*x^m+b*(-1/2*I*Pi*(csgn(I*c)-csgn(I*c*x^n))*(csgn(I*x^n)-csgn(I*c*x^n))*csgn(I*c*x^n)+ln(c)+ln(x^n))^q)^2","C"
23,1,16321,18,2.886000," ","int((a/x^2+2*b*n*ln(c*x^n)/x^3)*(a*x^2+b*x*ln(c*x^n)^2)^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
24,1,63,18,0.091000," ","int((a/x+2*b*n*ln(c*x^n)/x^2)*(a*x^2+b*x*ln(c*x^n)^2),x)","\frac{b^{2} \ln \left(c \,x^{n}\right)^{4}}{2}+2 a b n x \ln \left(c \,x^{n}\right)-2 a b n x \ln \left(c \,{\mathrm e}^{n \ln \left(x \right)}\right)+a b x \ln \left(c \,{\mathrm e}^{n \ln \left(x \right)}\right)^{2}+\frac{a^{2} x^{2}}{2}"," ",0,"1/2*a^2*x^2+a*b*x*ln(c*exp(n*ln(x)))^2-2*a*b*n*x*ln(c*exp(n*ln(x)))+1/2*b^2*ln(c*x^n)^4+2*ln(c*x^n)*a*b*n*x","B"
25,1,15,14,0.067000," ","int(a+2*b*n*ln(c*x^n)/x,x)","b \ln \left(c \,x^{n}\right)^{2}+a x"," ",0,"a*x+b*ln(c*x^n)^2","A"
26,1,432,15,0.288000," ","int((a*x+2*b*n*ln(c*x^n))/(a*x^2+b*x*ln(c*x^n)^2),x)","\ln \left(\ln \left(x^{n}\right)^{2}+\left(-i \pi  \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)+i \pi  \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i c \,x^{n}\right)^{2}+i \pi  \,\mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)^{2}-i \pi  \mathrm{csgn}\left(i c \,x^{n}\right)^{3}+2 \ln \left(c \right)\right) \ln \left(x^{n}\right)+\frac{-\pi^{2} b \mathrm{csgn}\left(i c \right)^{2} \mathrm{csgn}\left(i x^{n}\right)^{2} \mathrm{csgn}\left(i c \,x^{n}\right)^{2}+2 \pi^{2} b \mathrm{csgn}\left(i c \right)^{2} \mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)^{3}-\pi^{2} b \mathrm{csgn}\left(i c \right)^{2} \mathrm{csgn}\left(i c \,x^{n}\right)^{4}+2 \pi^{2} b \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i x^{n}\right)^{2} \mathrm{csgn}\left(i c \,x^{n}\right)^{3}-4 \pi^{2} b \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)^{4}+2 \pi^{2} b \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i c \,x^{n}\right)^{5}-\pi^{2} b \mathrm{csgn}\left(i x^{n}\right)^{2} \mathrm{csgn}\left(i c \,x^{n}\right)^{4}+2 \pi^{2} b \,\mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)^{5}-\pi^{2} b \mathrm{csgn}\left(i c \,x^{n}\right)^{6}-4 i \pi  b \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right) \ln \left(c \right)+4 i \pi  b \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i c \,x^{n}\right)^{2} \ln \left(c \right)+4 i \pi  b \,\mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)^{2} \ln \left(c \right)-4 i \pi  b \mathrm{csgn}\left(i c \,x^{n}\right)^{3} \ln \left(c \right)+4 b \ln \left(c \right)^{2}+4 a x}{4 b}\right)"," ",0,"ln(1/4*(-b*Pi^2*csgn(I*x^n)^2*csgn(I*c*x^n)^4+2*b*Pi^2*csgn(I*x^n)^2*csgn(I*c*x^n)^3*csgn(I*c)-b*Pi^2*csgn(I*x^n)^2*csgn(I*c*x^n)^2*csgn(I*c)^2+2*b*Pi^2*csgn(I*x^n)*csgn(I*c*x^n)^5-4*b*Pi^2*csgn(I*x^n)*csgn(I*c*x^n)^4*csgn(I*c)+2*b*Pi^2*csgn(I*x^n)*csgn(I*c*x^n)^3*csgn(I*c)^2-b*Pi^2*csgn(I*c*x^n)^6+2*b*Pi^2*csgn(I*c*x^n)^5*csgn(I*c)-b*Pi^2*csgn(I*c*x^n)^4*csgn(I*c)^2+4*I*b*ln(c)*Pi*csgn(I*x^n)*csgn(I*c*x^n)^2-4*I*b*ln(c)*Pi*csgn(I*x^n)*csgn(I*c*x^n)*csgn(I*c)-4*I*b*ln(c)*Pi*csgn(I*c*x^n)^3+4*I*b*ln(c)*Pi*csgn(I*c*x^n)^2*csgn(I*c)+4*b*ln(c)^2+4*a*x)/b+(I*Pi*csgn(I*x^n)*csgn(I*c*x^n)^2-I*Pi*csgn(I*x^n)*csgn(I*c*x^n)*csgn(I*c)-I*Pi*csgn(I*c*x^n)^3+I*Pi*csgn(I*c*x^n)^2*csgn(I*c)+2*ln(c))*ln(x^n)+ln(x^n)^2)","C"
27,1,451,18,0.306000," ","int((a*x^2+2*b*n*x*ln(c*x^n))/(a*x^2+b*x*ln(c*x^n)^2)^2,x)","-\frac{4}{-\pi^{2} b \mathrm{csgn}\left(i c \right)^{2} \mathrm{csgn}\left(i x^{n}\right)^{2} \mathrm{csgn}\left(i c \,x^{n}\right)^{2}+2 \pi^{2} b \mathrm{csgn}\left(i c \right)^{2} \mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)^{3}-\pi^{2} b \mathrm{csgn}\left(i c \right)^{2} \mathrm{csgn}\left(i c \,x^{n}\right)^{4}+2 \pi^{2} b \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i x^{n}\right)^{2} \mathrm{csgn}\left(i c \,x^{n}\right)^{3}-4 \pi^{2} b \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)^{4}+2 \pi^{2} b \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i c \,x^{n}\right)^{5}-\pi^{2} b \mathrm{csgn}\left(i x^{n}\right)^{2} \mathrm{csgn}\left(i c \,x^{n}\right)^{4}+2 \pi^{2} b \,\mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)^{5}-\pi^{2} b \mathrm{csgn}\left(i c \,x^{n}\right)^{6}-4 i \pi  b \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right) \ln \left(c \right)-4 i \pi  b \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right) \ln \left(x^{n}\right)+4 i \pi  b \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i c \,x^{n}\right)^{2} \ln \left(c \right)+4 i \pi  b \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i c \,x^{n}\right)^{2} \ln \left(x^{n}\right)+4 i \pi  b \,\mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)^{2} \ln \left(c \right)+4 i \pi  b \,\mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)^{2} \ln \left(x^{n}\right)-4 i \pi  b \mathrm{csgn}\left(i c \,x^{n}\right)^{3} \ln \left(c \right)-4 i \pi  b \mathrm{csgn}\left(i c \,x^{n}\right)^{3} \ln \left(x^{n}\right)+4 b \ln \left(c \right)^{2}+8 b \ln \left(c \right) \ln \left(x^{n}\right)+4 b \ln \left(x^{n}\right)^{2}+4 a x}"," ",0,"-4/(-Pi^2*b*csgn(I*x^n)^2*csgn(I*c*x^n)^4+2*Pi^2*b*csgn(I*c)*csgn(I*x^n)^2*csgn(I*c*x^n)^3-Pi^2*b*csgn(I*c)^2*csgn(I*x^n)^2*csgn(I*c*x^n)^2+2*Pi^2*b*csgn(I*x^n)*csgn(I*c*x^n)^5-4*Pi^2*b*csgn(I*c)*csgn(I*x^n)*csgn(I*c*x^n)^4+2*Pi^2*b*csgn(I*c)^2*csgn(I*x^n)*csgn(I*c*x^n)^3-Pi^2*b*csgn(I*c*x^n)^6+2*Pi^2*b*csgn(I*c)*csgn(I*c*x^n)^5-Pi^2*b*csgn(I*c)^2*csgn(I*c*x^n)^4+4*I*b*ln(x^n)*Pi*csgn(I*x^n)*csgn(I*c*x^n)^2+4*I*b*ln(x^n)*Pi*csgn(I*c*x^n)^2*csgn(I*c)-4*I*Pi*b*csgn(I*c*x^n)^3*ln(c)-4*I*b*ln(x^n)*Pi*csgn(I*c*x^n)^3-4*I*b*ln(x^n)*Pi*csgn(I*x^n)*csgn(I*c*x^n)*csgn(I*c)+4*I*Pi*b*csgn(I*x^n)*csgn(I*c*x^n)^2*ln(c)+4*I*Pi*b*csgn(I*c)*csgn(I*c*x^n)^2*ln(c)-4*I*Pi*b*csgn(I*c)*csgn(I*x^n)*csgn(I*c*x^n)*ln(c)+4*b*ln(c)^2+8*b*ln(c)*ln(x^n)+4*b*ln(x^n)^2+4*a*x)","C"
28,1,447,18,0.317000," ","int((a*x^3+2*b*n*x^2*ln(c*x^n))/(a*x^2+b*x*ln(c*x^n)^2)^3,x)","-\frac{8}{\left(\pi^{2} b \mathrm{csgn}\left(i c \right)^{2} \mathrm{csgn}\left(i x^{n}\right)^{2} \mathrm{csgn}\left(i c \,x^{n}\right)^{2}-2 \pi^{2} b \mathrm{csgn}\left(i c \right)^{2} \mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)^{3}+\pi^{2} b \mathrm{csgn}\left(i c \right)^{2} \mathrm{csgn}\left(i c \,x^{n}\right)^{4}-2 \pi^{2} b \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i x^{n}\right)^{2} \mathrm{csgn}\left(i c \,x^{n}\right)^{3}+4 \pi^{2} b \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)^{4}-2 \pi^{2} b \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i c \,x^{n}\right)^{5}+\pi^{2} b \mathrm{csgn}\left(i x^{n}\right)^{2} \mathrm{csgn}\left(i c \,x^{n}\right)^{4}-2 \pi^{2} b \,\mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)^{5}+\pi^{2} b \mathrm{csgn}\left(i c \,x^{n}\right)^{6}+4 i \pi  b \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right) \ln \left(c \right)+4 i \pi  b \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right) \ln \left(x^{n}\right)-4 i \pi  b \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i c \,x^{n}\right)^{2} \ln \left(c \right)-4 i \pi  b \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i c \,x^{n}\right)^{2} \ln \left(x^{n}\right)-4 i \pi  b \,\mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)^{2} \ln \left(c \right)-4 i \pi  b \,\mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)^{2} \ln \left(x^{n}\right)+4 i \pi  b \mathrm{csgn}\left(i c \,x^{n}\right)^{3} \ln \left(c \right)+4 i \pi  b \mathrm{csgn}\left(i c \,x^{n}\right)^{3} \ln \left(x^{n}\right)-4 b \ln \left(c \right)^{2}-8 b \ln \left(c \right) \ln \left(x^{n}\right)-4 b \ln \left(x^{n}\right)^{2}-4 a x \right)^{2}}"," ",0,"-8/(Pi^2*b*csgn(I*x^n)^2*csgn(I*c*x^n)^4-2*Pi^2*b*csgn(I*c)*csgn(I*x^n)^2*csgn(I*c*x^n)^3+Pi^2*b*csgn(I*c)^2*csgn(I*x^n)^2*csgn(I*c*x^n)^2-2*Pi^2*b*csgn(I*x^n)*csgn(I*c*x^n)^5+4*Pi^2*b*csgn(I*c)*csgn(I*x^n)*csgn(I*c*x^n)^4-2*Pi^2*b*csgn(I*c)^2*csgn(I*x^n)*csgn(I*c*x^n)^3+Pi^2*b*csgn(I*c*x^n)^6-2*Pi^2*b*csgn(I*c)*csgn(I*c*x^n)^5+Pi^2*b*csgn(I*c)^2*csgn(I*c*x^n)^4+4*I*b*ln(x^n)*Pi*csgn(I*x^n)*csgn(I*c*x^n)*csgn(I*c)+4*I*b*ln(x^n)*Pi*csgn(I*c*x^n)^3+4*I*b*ln(c)*Pi*csgn(I*x^n)*csgn(I*c*x^n)*csgn(I*c)-4*I*b*ln(x^n)*Pi*csgn(I*x^n)*csgn(I*c*x^n)^2-4*I*b*ln(c)*Pi*csgn(I*c*x^n)^2*csgn(I*c)-4*I*b*ln(c)*Pi*csgn(I*x^n)*csgn(I*c*x^n)^2-4*I*b*ln(x^n)*Pi*csgn(I*c*x^n)^2*csgn(I*c)+4*I*b*ln(c)*Pi*csgn(I*c*x^n)^3-4*b*ln(c)^2-8*b*ln(c)*ln(x^n)-4*b*ln(x^n)^2-4*a*x)^2","C"
29,1,215,19,0.602000," ","int((a*(m-1)*x^(m-1)+b*n*q*ln(c*x^n)^(q-1))/(a*x^m+b*x*ln(c*x^n)^q),x)","-q \ln \left(-\frac{i \pi  \left(\mathrm{csgn}\left(i c \right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \left(\mathrm{csgn}\left(i x^{n}\right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \mathrm{csgn}\left(i c \,x^{n}\right)}{2}+\ln \left(c \right)+\ln \left(x^{n}\right)\right)+q \ln \left(-\frac{i \pi  \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)}{2}+\frac{i \pi  \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i c \,x^{n}\right)^{2}}{2}+\frac{i \pi  \,\mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)^{2}}{2}-\frac{i \pi  \mathrm{csgn}\left(i c \,x^{n}\right)^{3}}{2}+\ln \left(c \right)+\ln \left(x^{n}\right)\right)+\ln \left(\left(-\frac{i \pi  \left(\mathrm{csgn}\left(i c \right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \left(\mathrm{csgn}\left(i x^{n}\right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \mathrm{csgn}\left(i c \,x^{n}\right)}{2}+\ln \left(c \right)+\ln \left(x^{n}\right)\right)^{q}+\frac{a \,x^{m}}{b x}\right)"," ",0,"q*ln(ln(c)+ln(x^n)-1/2*I*Pi*csgn(I*c*x^n)^3+1/2*I*Pi*csgn(I*c*x^n)^2*csgn(I*c)+1/2*I*Pi*csgn(I*x^n)*csgn(I*c*x^n)^2-1/2*I*Pi*csgn(I*c*x^n)*csgn(I*c)*csgn(I*x^n))-q*ln(-1/2*I*Pi*(csgn(I*c)-csgn(I*c*x^n))*(csgn(I*x^n)-csgn(I*c*x^n))*csgn(I*c*x^n)+ln(c)+ln(x^n))+ln((-1/2*I*Pi*(csgn(I*c)-csgn(I*c*x^n))*(csgn(I*x^n)-csgn(I*c*x^n))*csgn(I*c*x^n)+ln(c)+ln(x^n))^q+1/x*a*x^m/b)","C"
30,0,0,80,0.896000," ","int((d*x^m+e*ln(c*x^n)^(q-1))*(a*x^m+b*ln(c*x^n)^q)^p/x,x)","\int \frac{\left(d \,x^{m}+e \ln \left(c \,x^{n}\right)^{q -1}\right) \left(a \,x^{m}+b \ln \left(c \,x^{n}\right)^{q}\right)^{p}}{x}\, dx"," ",0,"int((d*x^m+e*ln(c*x^n)^(q-1))*(a*x^m+b*ln(c*x^n)^q)^p/x,x)","F"
31,0,0,336,52.591000," ","int((d*x^m+e*ln(c*x^n)^(q-1))*(a*x^m+b*ln(c*x^n)^q)^3/x,x)","\int \frac{\left(d \,x^{m}+e \ln \left(c \,x^{n}\right)^{q -1}\right) \left(a \,x^{m}+b \ln \left(c \,x^{n}\right)^{q}\right)^{3}}{x}\, dx"," ",0,"int((d*x^m+e*ln(c*x^n)^(q-1))*(a*x^m+b*ln(c*x^n)^q)^3/x,x)","F"
32,0,0,236,111.813000," ","int((d*x^m+e*ln(c*x^n)^(q-1))*(a*x^m+b*ln(c*x^n)^q)^2/x,x)","\int \frac{\left(d \,x^{m}+e \ln \left(c \,x^{n}\right)^{q -1}\right) \left(a \,x^{m}+b \ln \left(c \,x^{n}\right)^{q}\right)^{2}}{x}\, dx"," ",0,"int((d*x^m+e*ln(c*x^n)^(q-1))*(a*x^m+b*ln(c*x^n)^q)^2/x,x)","F"
33,0,0,136,73.293000," ","int((d*x^m+e*ln(c*x^n)^(q-1))*(a*x^m+b*ln(c*x^n)^q)/x,x)","\int \frac{\left(d \,x^{m}+e \ln \left(c \,x^{n}\right)^{q -1}\right) \left(a \,x^{m}+b \ln \left(c \,x^{n}\right)^{q}\right)}{x}\, dx"," ",0,"int((d*x^m+e*ln(c*x^n)^(q-1))*(a*x^m+b*ln(c*x^n)^q)/x,x)","F"
34,1,26,25,0.082000," ","int((d*x^m+e*ln(c*x^n)^(q-1))/x,x)","\frac{d \,x^{m}}{m}+\frac{e \ln \left(c \,x^{n}\right)^{q}}{n q}"," ",0,"d*x^m/m+e*ln(c*x^n)^q/n/q","A"
35,0,0,72,114.838000," ","int((d*x^m+e*ln(c*x^n)^(q-1))/x/(a*x^m+b*ln(c*x^n)^q),x)","\int \frac{d \,x^{m}+e \ln \left(c \,x^{n}\right)^{q -1}}{\left(a \,x^{m}+b \ln \left(c \,x^{n}\right)^{q}\right) x}\, dx"," ",0,"int((d*x^m+e*ln(c*x^n)^(q-1))/x/(a*x^m+b*ln(c*x^n)^q),x)","F"
36,0,0,74,51.280000," ","int((d*x^m+e*ln(c*x^n)^(q-1))/x/(a*x^m+b*ln(c*x^n)^q)^2,x)","\int \frac{d \,x^{m}+e \ln \left(c \,x^{n}\right)^{q -1}}{\left(a \,x^{m}+b \ln \left(c \,x^{n}\right)^{q}\right)^{2} x}\, dx"," ",0,"int((d*x^m+e*ln(c*x^n)^(q-1))/x/(a*x^m+b*ln(c*x^n)^q)^2,x)","F"
37,0,0,74,148.516000," ","int((d*x^m+e*ln(c*x^n)^(q-1))/x/(a*x^m+b*ln(c*x^n)^q)^3,x)","\int \frac{d \,x^{m}+e \ln \left(c \,x^{n}\right)^{q -1}}{\left(a \,x^{m}+b \ln \left(c \,x^{n}\right)^{q}\right)^{3} x}\, dx"," ",0,"int((d*x^m+e*ln(c*x^n)^(q-1))/x/(a*x^m+b*ln(c*x^n)^q)^3,x)","F"
38,1,158,26,0.512000," ","int((a*d*n*x^m-a*d*m*x^m*ln(c*x^n)-b*d*n*(q-1)*ln(c*x^n)^q)/x/(a*x^m+b*ln(c*x^n)^q)^2,x)","\frac{\left(-i \pi  \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)+i \pi  \,\mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i c \,x^{n}\right)^{2}+i \pi  \,\mathrm{csgn}\left(i x^{n}\right) \mathrm{csgn}\left(i c \,x^{n}\right)^{2}-i \pi  \mathrm{csgn}\left(i c \,x^{n}\right)^{3}+2 \ln \left(c \right)+2 \ln \left(x^{n}\right)\right) d}{2 a \,x^{m}+2 b \left(-\frac{i \pi  \left(\mathrm{csgn}\left(i c \right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \left(\mathrm{csgn}\left(i x^{n}\right)-\mathrm{csgn}\left(i c \,x^{n}\right)\right) \mathrm{csgn}\left(i c \,x^{n}\right)}{2}+\ln \left(c \right)+\ln \left(x^{n}\right)\right)^{q}}"," ",0,"1/2*(2*ln(c)+2*ln(x^n)+I*Pi*csgn(I*x^n)*csgn(I*c*x^n)^2-I*Pi*csgn(I*x^n)*csgn(I*c*x^n)*csgn(I*c)-I*Pi*csgn(I*c*x^n)^3+I*Pi*csgn(I*c*x^n)^2*csgn(I*c))*d/(a*x^m+b*(-1/2*I*Pi*(csgn(I*c)-csgn(I*c*x^n))*(csgn(I*x^n)-csgn(I*c*x^n))*csgn(I*c*x^n)+ln(c)+ln(x^n))^q)","C"
39,0,0,60,3.260000," ","int((n*q-ln(c*x^n))/(a*x+b*ln(c*x^n)^q)^2,x)","\int \frac{n q -\ln \left(c \,x^{n}\right)}{\left(a x +b \ln \left(c \,x^{n}\right)^{q}\right)^{2}}\, dx"," ",0,"int((n*q-ln(c*x^n))/(a*x+b*ln(c*x^n)^q)^2,x)","F"
40,-2,0,43,180.000000," ","int(ln(2*x*(e*x+d*(-e/d)^(1/2))/(e*x^2+d))/(e*x^2+d),x)","\int \frac{\ln \left(\frac{2 \left(e x +\sqrt{-\frac{e}{d}}\, d \right) x}{e \,x^{2}+d}\right)}{e \,x^{2}+d}\, dx"," ",0,"int(ln(2*x*(e*x+d*(-e/d)^(1/2))/(e*x^2+d))/(e*x^2+d),x)","F"
41,-2,0,44,180.000000," ","int(ln(-2*x*(-e*x+(-1/d*e)^(1/2)*d)/(e*x^2+d))/(e*x^2+d),x)","\int \frac{\ln \left(-\frac{2 \left(-e x +\sqrt{-\frac{e}{d}}\, d \right) x}{e \,x^{2}+d}\right)}{e \,x^{2}+d}\, dx"," ",0,"int(ln(-2*x*(-e*x+(-1/d*e)^(1/2)*d)/(e*x^2+d))/(e*x^2+d),x)","F"
42,-2,0,41,180.000000," ","int(ln(2*x*(e*x+d*e^(1/2)/(-d)^(1/2))/(e*x^2+d))/(e*x^2+d),x)","\int \frac{\ln \left(\frac{2 \left(e x +\frac{d \sqrt{e}}{\sqrt{-d}}\right) x}{e \,x^{2}+d}\right)}{e \,x^{2}+d}\, dx"," ",0,"int(ln(2*x*(e*x+d*e^(1/2)/(-d)^(1/2))/(e*x^2+d))/(e*x^2+d),x)","F"
43,-2,0,40,180.000000," ","int(ln(-2*x*(-e*x+1/(-d)^(1/2)*d*e^(1/2))/(e*x^2+d))/(e*x^2+d),x)","\int \frac{\ln \left(-\frac{2 \left(-e x +\frac{d \sqrt{e}}{\sqrt{-d}}\right) x}{e \,x^{2}+d}\right)}{e \,x^{2}+d}\, dx"," ",0,"int(ln(-2*x*(-e*x+1/(-d)^(1/2)*d*e^(1/2))/(e*x^2+d))/(e*x^2+d),x)","F"
44,-2,0,39,180.000000," ","int(ln(2*x*(e*x+d^(1/2)*(-e)^(1/2))/(e*x^2+d))/(e*x^2+d),x)","\int \frac{\ln \left(\frac{2 \left(e x +\sqrt{-e}\, \sqrt{d}\right) x}{e \,x^{2}+d}\right)}{e \,x^{2}+d}\, dx"," ",0,"int(ln(2*x*(e*x+d^(1/2)*(-e)^(1/2))/(e*x^2+d))/(e*x^2+d),x)","F"
45,-2,0,40,180.000000," ","int(ln(-2*x*(-e*x+(-e)^(1/2)*d^(1/2))/(e*x^2+d))/(e*x^2+d),x)","\int \frac{\ln \left(-\frac{2 \left(-e x +\sqrt{-e}\, \sqrt{d}\right) x}{e \,x^{2}+d}\right)}{e \,x^{2}+d}\, dx"," ",0,"int(ln(-2*x*(-e*x+(-e)^(1/2)*d^(1/2))/(e*x^2+d))/(e*x^2+d),x)","F"
46,-1,0,67,180.000000," ","int((e*x)^m*(a+b*ln(c*ln(d*x)^p)),x)","\int \left(b \ln \left(c \ln \left(d x \right)^{p}\right)+a \right) \left(e x \right)^{m}\, dx"," ",0,"int((e*x)^m*(a+b*ln(c*ln(d*x)^p)),x)","F"
47,0,0,80,2.589000," ","int((e*x)^m*(a+b*ln(c*ln(d*x^n)^p)),x)","\int \left(b \ln \left(c \ln \left(d \,x^{n}\right)^{p}\right)+a \right) \left(e x \right)^{m}\, dx"," ",0,"int((e*x)^m*(a+b*ln(c*ln(d*x^n)^p)),x)","F"
48,0,0,53,0.464000," ","int(x^2*(b*ln(c*ln(d*x^n)^p)+a),x)","\int \left(b \ln \left(c \ln \left(d \,x^{n}\right)^{p}\right)+a \right) x^{2}\, dx"," ",0,"int(x^2*(b*ln(c*ln(d*x^n)^p)+a),x)","F"
49,0,0,53,0.464000," ","int(x*(b*ln(c*ln(d*x^n)^p)+a),x)","\int \left(b \ln \left(c \ln \left(d \,x^{n}\right)^{p}\right)+a \right) x\, dx"," ",0,"int(x*(b*ln(c*ln(d*x^n)^p)+a),x)","F"
50,0,0,45,0.513000," ","int(b*ln(c*ln(d*x^n)^p)+a,x)","\int b \ln \left(c \ln \left(d \,x^{n}\right)^{p}\right)+a\, dx"," ",0,"int(b*ln(c*ln(d*x^n)^p)+a,x)","F"
51,1,48,32,0.077000," ","int((b*ln(c*ln(d*x^n)^p)+a)/x,x)","-\frac{b p \ln \left(d \,x^{n}\right)}{n}+\frac{b \ln \left(c \ln \left(d \,x^{n}\right)^{p}\right) \ln \left(d \,x^{n}\right)}{n}+\frac{a \ln \left(d \,x^{n}\right)}{n}"," ",0,"1/n*ln(c*ln(d*x^n)^p)*ln(d*x^n)*b-1/n*ln(d*x^n)*b*p+1/n*a*ln(d*x^n)","A"
52,0,0,50,0.461000," ","int((b*ln(c*ln(d*x^n)^p)+a)/x^2,x)","\int \frac{b \ln \left(c \ln \left(d \,x^{n}\right)^{p}\right)+a}{x^{2}}\, dx"," ",0,"int((b*ln(c*ln(d*x^n)^p)+a)/x^2,x)","F"
53,0,0,54,0.437000," ","int((b*ln(c*ln(d*x^n)^p)+a)/x^3,x)","\int \frac{b \ln \left(c \ln \left(d \,x^{n}\right)^{p}\right)+a}{x^{3}}\, dx"," ",0,"int((b*ln(c*ln(d*x^n)^p)+a)/x^3,x)","F"
54,0,0,54,0.441000," ","int((b*ln(c*ln(d*x^n)^p)+a)/x^4,x)","\int \frac{b \ln \left(c \ln \left(d \,x^{n}\right)^{p}\right)+a}{x^{4}}\, dx"," ",0,"int((b*ln(c*ln(d*x^n)^p)+a)/x^4,x)","F"
55,1,26,22,0.086000," ","int(ln(c*ln(d*x)^p),x)","x \ln \left(c \ln \left(d x \right)^{p}\right)+\frac{p \Ei \left(1, -\ln \left(d x \right)\right)}{d}"," ",0,"x*ln(c*ln(d*x)^p)+p/d*Ei(1,-ln(d*x))","A"
56,1,23,20,0.070000," ","int(ln(c*ln(d*x)^p)/x,x)","-p \ln \left(d x \right)+\ln \left(c \ln \left(d x \right)^{p}\right) \ln \left(d x \right)"," ",0,"ln(d*x)*ln(c*ln(d*x)^p)-p*ln(d*x)","A"
57,0,0,40,0.424000," ","int(ln(c*ln(d*x^n)^p),x)","\int \ln \left(c \ln \left(d \,x^{n}\right)^{p}\right)\, dx"," ",0,"int(ln(c*ln(d*x^n)^p),x)","F"
58,1,35,27,0.074000," ","int(ln(c*ln(d*x^n)^p)/x,x)","-\frac{p \ln \left(d \,x^{n}\right)}{n}+\frac{\ln \left(c \ln \left(d \,x^{n}\right)^{p}\right) \ln \left(d \,x^{n}\right)}{n}"," ",0,"ln(d*x^n)*ln(c*ln(d*x^n)^p)/n-1/n*p*ln(d*x^n)","A"
59,-1,0,68,180.000000," ","int(x^m*ln(d*(c*x^2+b*x)^n),x)","\int x^{m} \ln \left(d \left(c \,x^{2}+b x \right)^{n}\right)\, dx"," ",0,"int(x^m*ln(d*(c*x^2+b*x)^n),x)","F"
60,0,0,85,0.171000," ","int(x^4*ln(d*(c*x^2+b*x)^n),x)","\int x^{4} \ln \left(d \left(c \,x^{2}+b x \right)^{n}\right)\, dx"," ",0,"int(x^4*ln(d*(c*x^2+b*x)^n),x)","F"
61,0,0,73,0.084000," ","int(x^3*ln(d*(c*x^2+b*x)^n),x)","\int x^{3} \ln \left(d \left(c \,x^{2}+b x \right)^{n}\right)\, dx"," ",0,"int(x^3*ln(d*(c*x^2+b*x)^n),x)","F"
62,0,0,61,0.086000," ","int(x^2*ln(d*(c*x^2+b*x)^n),x)","\int x^{2} \ln \left(d \left(c \,x^{2}+b x \right)^{n}\right)\, dx"," ",0,"int(x^2*ln(d*(c*x^2+b*x)^n),x)","F"
63,0,0,49,0.107000," ","int(x*ln(d*(c*x^2+b*x)^n),x)","\int x \ln \left(d \left(c \,x^{2}+b x \right)^{n}\right)\, dx"," ",0,"int(x*ln(d*(c*x^2+b*x)^n),x)","F"
64,1,34,33,0.074000," ","int(ln(d*(c*x^2+b*x)^n),x)","\frac{b n \ln \left(c x +b \right)}{c}-2 n x +x \ln \left(d \left(c \,x^{2}+b x \right)^{n}\right)"," ",0,"-2*n*x+b*n*ln(c*x+b)/c+x*ln(d*(c*x^2+b*x)^n)","A"
65,0,0,51,0.109000," ","int(ln(d*(c*x^2+b*x)^n)/x,x)","\int \frac{\ln \left(d \left(c \,x^{2}+b x \right)^{n}\right)}{x}\, dx"," ",0,"int(ln(d*(c*x^2+b*x)^n)/x,x)","F"
66,0,0,47,0.090000," ","int(ln(d*(c*x^2+b*x)^n)/x^2,x)","\int \frac{\ln \left(d \left(c \,x^{2}+b x \right)^{n}\right)}{x^{2}}\, dx"," ",0,"int(ln(d*(c*x^2+b*x)^n)/x^2,x)","F"
67,0,0,62,0.082000," ","int(ln(d*(c*x^2+b*x)^n)/x^3,x)","\int \frac{\ln \left(d \left(c \,x^{2}+b x \right)^{n}\right)}{x^{3}}\, dx"," ",0,"int(ln(d*(c*x^2+b*x)^n)/x^3,x)","F"
68,0,0,74,0.082000," ","int(ln(d*(c*x^2+b*x)^n)/x^4,x)","\int \frac{\ln \left(d \left(c \,x^{2}+b x \right)^{n}\right)}{x^{4}}\, dx"," ",0,"int(ln(d*(c*x^2+b*x)^n)/x^4,x)","F"
69,0,0,86,0.086000," ","int(ln(d*(c*x^2+b*x)^n)/x^5,x)","\int \frac{\ln \left(d \left(c \,x^{2}+b x \right)^{n}\right)}{x^{5}}\, dx"," ",0,"int(ln(d*(c*x^2+b*x)^n)/x^5,x)","F"
70,0,0,153,1.399000," ","int(x^m*ln(d*(c*x^2+b*x+a)^n),x)","\int x^{m} \ln \left(d \left(c \,x^{2}+b x +a \right)^{n}\right)\, dx"," ",0,"int(x^m*ln(d*(c*x^2+b*x+a)^n),x)","F"
71,1,1621,187,0.811000," ","int(x^4*ln(d*(c*x^2+b*x+a)^n),x)","-\frac{i \pi  \,x^{5} \mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)}{10}+\frac{i \pi  \,x^{5} \mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}}{10}+\frac{i \pi  \,x^{5} \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}}{10}-\frac{i \pi  \,x^{5} \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{3}}{10}-\frac{2 n \,x^{5}}{25}+\frac{x^{5} \ln \left(d \right)}{5}+\frac{x^{5} \ln \left(\left(c \,x^{2}+b x +a \right)^{n}\right)}{5}+\frac{b n \,x^{4}}{20 c}+\frac{2 a n \,x^{3}}{15 c}-\frac{b^{2} n \,x^{3}}{15 c^{2}}-\frac{3 a b n \,x^{2}}{10 c^{2}}+\frac{b^{3} n \,x^{2}}{10 c^{3}}+\frac{a^{2} b n \ln \left(4 a^{3} c^{3}-13 a^{2} b^{2} c^{2}+7 a \,b^{4} c -b^{6}-2 \sqrt{-4 c^{5} a^{5}+25 a^{4} b^{2} c^{4}-50 a^{3} b^{4} c^{3}+35 a^{2} b^{6} c^{2}-10 a \,b^{8} c +b^{10}}\, c x -\sqrt{-4 c^{5} a^{5}+25 a^{4} b^{2} c^{4}-50 a^{3} b^{4} c^{3}+35 a^{2} b^{6} c^{2}-10 a \,b^{8} c +b^{10}}\, b \right)}{2 c^{3}}+\frac{a^{2} b n \ln \left(4 a^{3} c^{3}-13 a^{2} b^{2} c^{2}+7 a \,b^{4} c -b^{6}+2 \sqrt{-4 c^{5} a^{5}+25 a^{4} b^{2} c^{4}-50 a^{3} b^{4} c^{3}+35 a^{2} b^{6} c^{2}-10 a \,b^{8} c +b^{10}}\, c x +\sqrt{-4 c^{5} a^{5}+25 a^{4} b^{2} c^{4}-50 a^{3} b^{4} c^{3}+35 a^{2} b^{6} c^{2}-10 a \,b^{8} c +b^{10}}\, b \right)}{2 c^{3}}-\frac{2 a^{2} n x}{5 c^{2}}-\frac{a \,b^{3} n \ln \left(4 a^{3} c^{3}-13 a^{2} b^{2} c^{2}+7 a \,b^{4} c -b^{6}-2 \sqrt{-4 c^{5} a^{5}+25 a^{4} b^{2} c^{4}-50 a^{3} b^{4} c^{3}+35 a^{2} b^{6} c^{2}-10 a \,b^{8} c +b^{10}}\, c x -\sqrt{-4 c^{5} a^{5}+25 a^{4} b^{2} c^{4}-50 a^{3} b^{4} c^{3}+35 a^{2} b^{6} c^{2}-10 a \,b^{8} c +b^{10}}\, b \right)}{2 c^{4}}-\frac{a \,b^{3} n \ln \left(4 a^{3} c^{3}-13 a^{2} b^{2} c^{2}+7 a \,b^{4} c -b^{6}+2 \sqrt{-4 c^{5} a^{5}+25 a^{4} b^{2} c^{4}-50 a^{3} b^{4} c^{3}+35 a^{2} b^{6} c^{2}-10 a \,b^{8} c +b^{10}}\, c x +\sqrt{-4 c^{5} a^{5}+25 a^{4} b^{2} c^{4}-50 a^{3} b^{4} c^{3}+35 a^{2} b^{6} c^{2}-10 a \,b^{8} c +b^{10}}\, b \right)}{2 c^{4}}+\frac{4 a \,b^{2} n x}{5 c^{3}}+\frac{b^{5} n \ln \left(4 a^{3} c^{3}-13 a^{2} b^{2} c^{2}+7 a \,b^{4} c -b^{6}-2 \sqrt{-4 c^{5} a^{5}+25 a^{4} b^{2} c^{4}-50 a^{3} b^{4} c^{3}+35 a^{2} b^{6} c^{2}-10 a \,b^{8} c +b^{10}}\, c x -\sqrt{-4 c^{5} a^{5}+25 a^{4} b^{2} c^{4}-50 a^{3} b^{4} c^{3}+35 a^{2} b^{6} c^{2}-10 a \,b^{8} c +b^{10}}\, b \right)}{10 c^{5}}+\frac{b^{5} n \ln \left(4 a^{3} c^{3}-13 a^{2} b^{2} c^{2}+7 a \,b^{4} c -b^{6}+2 \sqrt{-4 c^{5} a^{5}+25 a^{4} b^{2} c^{4}-50 a^{3} b^{4} c^{3}+35 a^{2} b^{6} c^{2}-10 a \,b^{8} c +b^{10}}\, c x +\sqrt{-4 c^{5} a^{5}+25 a^{4} b^{2} c^{4}-50 a^{3} b^{4} c^{3}+35 a^{2} b^{6} c^{2}-10 a \,b^{8} c +b^{10}}\, b \right)}{10 c^{5}}-\frac{b^{4} n x}{5 c^{4}}+\frac{\sqrt{-4 c^{5} a^{5}+25 a^{4} b^{2} c^{4}-50 a^{3} b^{4} c^{3}+35 a^{2} b^{6} c^{2}-10 a \,b^{8} c +b^{10}}\, n \ln \left(4 a^{3} c^{3}-13 a^{2} b^{2} c^{2}+7 a \,b^{4} c -b^{6}-2 \sqrt{-4 c^{5} a^{5}+25 a^{4} b^{2} c^{4}-50 a^{3} b^{4} c^{3}+35 a^{2} b^{6} c^{2}-10 a \,b^{8} c +b^{10}}\, c x -\sqrt{-4 c^{5} a^{5}+25 a^{4} b^{2} c^{4}-50 a^{3} b^{4} c^{3}+35 a^{2} b^{6} c^{2}-10 a \,b^{8} c +b^{10}}\, b \right)}{10 c^{5}}-\frac{\sqrt{-4 c^{5} a^{5}+25 a^{4} b^{2} c^{4}-50 a^{3} b^{4} c^{3}+35 a^{2} b^{6} c^{2}-10 a \,b^{8} c +b^{10}}\, n \ln \left(4 a^{3} c^{3}-13 a^{2} b^{2} c^{2}+7 a \,b^{4} c -b^{6}+2 \sqrt{-4 c^{5} a^{5}+25 a^{4} b^{2} c^{4}-50 a^{3} b^{4} c^{3}+35 a^{2} b^{6} c^{2}-10 a \,b^{8} c +b^{10}}\, c x +\sqrt{-4 c^{5} a^{5}+25 a^{4} b^{2} c^{4}-50 a^{3} b^{4} c^{3}+35 a^{2} b^{6} c^{2}-10 a \,b^{8} c +b^{10}}\, b \right)}{10 c^{5}}"," ",0,"1/5*x^5*ln((c*x^2+b*x+a)^n)+1/10*I*Pi*x^5*csgn(I*d)*csgn(I*d*(c*x^2+b*x+a)^n)^2+1/10*I*Pi*x^5*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)^2-1/10*I*Pi*x^5*csgn(I*d*(c*x^2+b*x+a)^n)^3-1/10*I*Pi*x^5*csgn(I*d)*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)+1/5*ln(d)*x^5-2/25*n*x^5+1/20*b*n*x^4/c+2/15/c*a*n*x^3-1/15*b^2*n*x^3/c^2-3/10/c^2*a*b*n*x^2+1/10*b^3*n*x^2/c^3+1/2/c^3*n*ln(4*a^3*c^3-13*a^2*b^2*c^2+7*a*b^4*c-b^6+2*(-4*a^5*c^5+25*a^4*b^2*c^4-50*a^3*b^4*c^3+35*a^2*b^6*c^2-10*a*b^8*c+b^10)^(1/2)*c*x+(-4*a^5*c^5+25*a^4*b^2*c^4-50*a^3*b^4*c^3+35*a^2*b^6*c^2-10*a*b^8*c+b^10)^(1/2)*b)*a^2*b-1/2/c^4*n*ln(4*a^3*c^3-13*a^2*b^2*c^2+7*a*b^4*c-b^6+2*(-4*a^5*c^5+25*a^4*b^2*c^4-50*a^3*b^4*c^3+35*a^2*b^6*c^2-10*a*b^8*c+b^10)^(1/2)*c*x+(-4*a^5*c^5+25*a^4*b^2*c^4-50*a^3*b^4*c^3+35*a^2*b^6*c^2-10*a*b^8*c+b^10)^(1/2)*b)*a*b^3+1/10/c^5*n*ln(4*a^3*c^3-13*a^2*b^2*c^2+7*a*b^4*c-b^6+2*(-4*a^5*c^5+25*a^4*b^2*c^4-50*a^3*b^4*c^3+35*a^2*b^6*c^2-10*a*b^8*c+b^10)^(1/2)*c*x+(-4*a^5*c^5+25*a^4*b^2*c^4-50*a^3*b^4*c^3+35*a^2*b^6*c^2-10*a*b^8*c+b^10)^(1/2)*b)*b^5+1/2/c^3*n*ln(4*a^3*c^3-13*a^2*b^2*c^2+7*a*b^4*c-b^6-2*(-4*a^5*c^5+25*a^4*b^2*c^4-50*a^3*b^4*c^3+35*a^2*b^6*c^2-10*a*b^8*c+b^10)^(1/2)*c*x-(-4*a^5*c^5+25*a^4*b^2*c^4-50*a^3*b^4*c^3+35*a^2*b^6*c^2-10*a*b^8*c+b^10)^(1/2)*b)*a^2*b-1/2/c^4*n*ln(4*a^3*c^3-13*a^2*b^2*c^2+7*a*b^4*c-b^6-2*(-4*a^5*c^5+25*a^4*b^2*c^4-50*a^3*b^4*c^3+35*a^2*b^6*c^2-10*a*b^8*c+b^10)^(1/2)*c*x-(-4*a^5*c^5+25*a^4*b^2*c^4-50*a^3*b^4*c^3+35*a^2*b^6*c^2-10*a*b^8*c+b^10)^(1/2)*b)*a*b^3+1/10/c^5*n*ln(4*a^3*c^3-13*a^2*b^2*c^2+7*a*b^4*c-b^6-2*(-4*a^5*c^5+25*a^4*b^2*c^4-50*a^3*b^4*c^3+35*a^2*b^6*c^2-10*a*b^8*c+b^10)^(1/2)*c*x-(-4*a^5*c^5+25*a^4*b^2*c^4-50*a^3*b^4*c^3+35*a^2*b^6*c^2-10*a*b^8*c+b^10)^(1/2)*b)*b^5-2/5/c^2*a^2*n*x+4/5/c^3*a*b^2*n*x-1/5*b^4*n*x/c^4-1/10/c^5*n*ln(4*a^3*c^3-13*a^2*b^2*c^2+7*a*b^4*c-b^6+2*(-4*a^5*c^5+25*a^4*b^2*c^4-50*a^3*b^4*c^3+35*a^2*b^6*c^2-10*a*b^8*c+b^10)^(1/2)*c*x+(-4*a^5*c^5+25*a^4*b^2*c^4-50*a^3*b^4*c^3+35*a^2*b^6*c^2-10*a*b^8*c+b^10)^(1/2)*b)*(-4*a^5*c^5+25*a^4*b^2*c^4-50*a^3*b^4*c^3+35*a^2*b^6*c^2-10*a*b^8*c+b^10)^(1/2)+1/10/c^5*n*ln(4*a^3*c^3-13*a^2*b^2*c^2+7*a*b^4*c-b^6-2*(-4*a^5*c^5+25*a^4*b^2*c^4-50*a^3*b^4*c^3+35*a^2*b^6*c^2-10*a*b^8*c+b^10)^(1/2)*c*x-(-4*a^5*c^5+25*a^4*b^2*c^4-50*a^3*b^4*c^3+35*a^2*b^6*c^2-10*a*b^8*c+b^10)^(1/2)*b)*(-4*a^5*c^5+25*a^4*b^2*c^4-50*a^3*b^4*c^3+35*a^2*b^6*c^2-10*a*b^8*c+b^10)^(1/2)","C"
72,1,1146,149,0.611000," ","int(x^3*ln(d*(c*x^2+b*x+a)^n),x)","-\frac{i \pi  \,x^{4} \mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)}{8}+\frac{i \pi  \,x^{4} \mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}}{8}+\frac{i \pi  \,x^{4} \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}}{8}-\frac{i \pi  \,x^{4} \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{3}}{8}-\frac{n \,x^{4}}{8}+\frac{x^{4} \ln \left(d \right)}{4}+\frac{x^{4} \ln \left(\left(c \,x^{2}+b x +a \right)^{n}\right)}{4}+\frac{b n \,x^{3}}{12 c}+\frac{a n \,x^{2}}{4 c}-\frac{b^{2} n \,x^{2}}{8 c^{2}}-\frac{a^{2} n \ln \left(8 a^{2} b \,c^{2}-6 a \,b^{3} c +b^{5}-2 \sqrt{-16 a^{3} b^{2} c^{3}+20 a^{2} b^{4} c^{2}-8 a \,b^{6} c +b^{8}}\, c x -\sqrt{-16 a^{3} b^{2} c^{3}+20 a^{2} b^{4} c^{2}-8 a \,b^{6} c +b^{8}}\, b \right)}{4 c^{2}}-\frac{a^{2} n \ln \left(8 a^{2} b \,c^{2}-6 a \,b^{3} c +b^{5}+2 \sqrt{-16 a^{3} b^{2} c^{3}+20 a^{2} b^{4} c^{2}-8 a \,b^{6} c +b^{8}}\, c x +\sqrt{-16 a^{3} b^{2} c^{3}+20 a^{2} b^{4} c^{2}-8 a \,b^{6} c +b^{8}}\, b \right)}{4 c^{2}}+\frac{a \,b^{2} n \ln \left(8 a^{2} b \,c^{2}-6 a \,b^{3} c +b^{5}-2 \sqrt{-16 a^{3} b^{2} c^{3}+20 a^{2} b^{4} c^{2}-8 a \,b^{6} c +b^{8}}\, c x -\sqrt{-16 a^{3} b^{2} c^{3}+20 a^{2} b^{4} c^{2}-8 a \,b^{6} c +b^{8}}\, b \right)}{2 c^{3}}+\frac{a \,b^{2} n \ln \left(8 a^{2} b \,c^{2}-6 a \,b^{3} c +b^{5}+2 \sqrt{-16 a^{3} b^{2} c^{3}+20 a^{2} b^{4} c^{2}-8 a \,b^{6} c +b^{8}}\, c x +\sqrt{-16 a^{3} b^{2} c^{3}+20 a^{2} b^{4} c^{2}-8 a \,b^{6} c +b^{8}}\, b \right)}{2 c^{3}}-\frac{3 a b n x}{4 c^{2}}-\frac{b^{4} n \ln \left(8 a^{2} b \,c^{2}-6 a \,b^{3} c +b^{5}-2 \sqrt{-16 a^{3} b^{2} c^{3}+20 a^{2} b^{4} c^{2}-8 a \,b^{6} c +b^{8}}\, c x -\sqrt{-16 a^{3} b^{2} c^{3}+20 a^{2} b^{4} c^{2}-8 a \,b^{6} c +b^{8}}\, b \right)}{8 c^{4}}-\frac{b^{4} n \ln \left(8 a^{2} b \,c^{2}-6 a \,b^{3} c +b^{5}+2 \sqrt{-16 a^{3} b^{2} c^{3}+20 a^{2} b^{4} c^{2}-8 a \,b^{6} c +b^{8}}\, c x +\sqrt{-16 a^{3} b^{2} c^{3}+20 a^{2} b^{4} c^{2}-8 a \,b^{6} c +b^{8}}\, b \right)}{8 c^{4}}+\frac{b^{3} n x}{4 c^{3}}+\frac{\sqrt{-16 a^{3} b^{2} c^{3}+20 a^{2} b^{4} c^{2}-8 a \,b^{6} c +b^{8}}\, n \ln \left(8 a^{2} b \,c^{2}-6 a \,b^{3} c +b^{5}-2 \sqrt{-16 a^{3} b^{2} c^{3}+20 a^{2} b^{4} c^{2}-8 a \,b^{6} c +b^{8}}\, c x -\sqrt{-16 a^{3} b^{2} c^{3}+20 a^{2} b^{4} c^{2}-8 a \,b^{6} c +b^{8}}\, b \right)}{8 c^{4}}-\frac{\sqrt{-16 a^{3} b^{2} c^{3}+20 a^{2} b^{4} c^{2}-8 a \,b^{6} c +b^{8}}\, n \ln \left(8 a^{2} b \,c^{2}-6 a \,b^{3} c +b^{5}+2 \sqrt{-16 a^{3} b^{2} c^{3}+20 a^{2} b^{4} c^{2}-8 a \,b^{6} c +b^{8}}\, c x +\sqrt{-16 a^{3} b^{2} c^{3}+20 a^{2} b^{4} c^{2}-8 a \,b^{6} c +b^{8}}\, b \right)}{8 c^{4}}"," ",0,"1/4*x^4*ln((c*x^2+b*x+a)^n)+1/8*I*Pi*x^4*csgn(I*d)*csgn(I*d*(c*x^2+b*x+a)^n)^2-1/8*I*Pi*x^4*csgn(I*d*(c*x^2+b*x+a)^n)^3-1/8*I*Pi*x^4*csgn(I*d)*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)+1/8*I*Pi*x^4*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)^2+1/4*ln(d)*x^4-1/8*n*x^4+1/12*b*n*x^3/c+1/4/c*a*n*x^2-1/8*b^2*n*x^2/c^2-1/4/c^2*n*ln(8*a^2*b*c^2-6*a*b^3*c+b^5+2*(-16*a^3*b^2*c^3+20*a^2*b^4*c^2-8*a*b^6*c+b^8)^(1/2)*c*x+(-16*a^3*b^2*c^3+20*a^2*b^4*c^2-8*a*b^6*c+b^8)^(1/2)*b)*a^2+1/2/c^3*n*ln(8*a^2*b*c^2-6*a*b^3*c+b^5+2*(-16*a^3*b^2*c^3+20*a^2*b^4*c^2-8*a*b^6*c+b^8)^(1/2)*c*x+(-16*a^3*b^2*c^3+20*a^2*b^4*c^2-8*a*b^6*c+b^8)^(1/2)*b)*a*b^2-1/8/c^4*n*ln(8*a^2*b*c^2-6*a*b^3*c+b^5+2*(-16*a^3*b^2*c^3+20*a^2*b^4*c^2-8*a*b^6*c+b^8)^(1/2)*c*x+(-16*a^3*b^2*c^3+20*a^2*b^4*c^2-8*a*b^6*c+b^8)^(1/2)*b)*b^4-1/4/c^2*n*ln(8*a^2*b*c^2-6*a*b^3*c+b^5-2*(-16*a^3*b^2*c^3+20*a^2*b^4*c^2-8*a*b^6*c+b^8)^(1/2)*c*x-(-16*a^3*b^2*c^3+20*a^2*b^4*c^2-8*a*b^6*c+b^8)^(1/2)*b)*a^2+1/2/c^3*n*ln(8*a^2*b*c^2-6*a*b^3*c+b^5-2*(-16*a^3*b^2*c^3+20*a^2*b^4*c^2-8*a*b^6*c+b^8)^(1/2)*c*x-(-16*a^3*b^2*c^3+20*a^2*b^4*c^2-8*a*b^6*c+b^8)^(1/2)*b)*a*b^2-1/8/c^4*n*ln(8*a^2*b*c^2-6*a*b^3*c+b^5-2*(-16*a^3*b^2*c^3+20*a^2*b^4*c^2-8*a*b^6*c+b^8)^(1/2)*c*x-(-16*a^3*b^2*c^3+20*a^2*b^4*c^2-8*a*b^6*c+b^8)^(1/2)*b)*b^4-3/4/c^2*a*b*n*x+1/4*b^3*n*x/c^3-1/8/c^4*n*ln(8*a^2*b*c^2-6*a*b^3*c+b^5+2*(-16*a^3*b^2*c^3+20*a^2*b^4*c^2-8*a*b^6*c+b^8)^(1/2)*c*x+(-16*a^3*b^2*c^3+20*a^2*b^4*c^2-8*a*b^6*c+b^8)^(1/2)*b)*(-16*a^3*b^2*c^3+20*a^2*b^4*c^2-8*a*b^6*c+b^8)^(1/2)+1/8/c^4*n*ln(8*a^2*b*c^2-6*a*b^3*c+b^5-2*(-16*a^3*b^2*c^3+20*a^2*b^4*c^2-8*a*b^6*c+b^8)^(1/2)*c*x-(-16*a^3*b^2*c^3+20*a^2*b^4*c^2-8*a*b^6*c+b^8)^(1/2)*b)*(-16*a^3*b^2*c^3+20*a^2*b^4*c^2-8*a*b^6*c+b^8)^(1/2)","C"
73,1,870,120,0.638000," ","int(x^2*ln(d*(c*x^2+b*x+a)^n),x)","-\frac{i \pi  \,x^{3} \mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)}{6}+\frac{i \pi  \,x^{3} \mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}}{6}+\frac{i \pi  \,x^{3} \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}}{6}-\frac{i \pi  \,x^{3} \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{3}}{6}-\frac{2 n \,x^{3}}{9}+\frac{x^{3} \ln \left(d \right)}{3}+\frac{x^{3} \ln \left(\left(c \,x^{2}+b x +a \right)^{n}\right)}{3}+\frac{b n \,x^{2}}{6 c}-\frac{a b n \ln \left(-4 a^{2} c^{2}+5 a \,b^{2} c -b^{4}-2 \sqrt{-4 a^{3} c^{3}+9 a^{2} b^{2} c^{2}-6 a \,b^{4} c +b^{6}}\, c x -\sqrt{-4 a^{3} c^{3}+9 a^{2} b^{2} c^{2}-6 a \,b^{4} c +b^{6}}\, b \right)}{2 c^{2}}-\frac{a b n \ln \left(-4 a^{2} c^{2}+5 a \,b^{2} c -b^{4}+2 \sqrt{-4 a^{3} c^{3}+9 a^{2} b^{2} c^{2}-6 a \,b^{4} c +b^{6}}\, c x +\sqrt{-4 a^{3} c^{3}+9 a^{2} b^{2} c^{2}-6 a \,b^{4} c +b^{6}}\, b \right)}{2 c^{2}}+\frac{2 a n x}{3 c}+\frac{b^{3} n \ln \left(-4 a^{2} c^{2}+5 a \,b^{2} c -b^{4}-2 \sqrt{-4 a^{3} c^{3}+9 a^{2} b^{2} c^{2}-6 a \,b^{4} c +b^{6}}\, c x -\sqrt{-4 a^{3} c^{3}+9 a^{2} b^{2} c^{2}-6 a \,b^{4} c +b^{6}}\, b \right)}{6 c^{3}}+\frac{b^{3} n \ln \left(-4 a^{2} c^{2}+5 a \,b^{2} c -b^{4}+2 \sqrt{-4 a^{3} c^{3}+9 a^{2} b^{2} c^{2}-6 a \,b^{4} c +b^{6}}\, c x +\sqrt{-4 a^{3} c^{3}+9 a^{2} b^{2} c^{2}-6 a \,b^{4} c +b^{6}}\, b \right)}{6 c^{3}}-\frac{b^{2} n x}{3 c^{2}}+\frac{\sqrt{-4 a^{3} c^{3}+9 a^{2} b^{2} c^{2}-6 a \,b^{4} c +b^{6}}\, n \ln \left(-4 a^{2} c^{2}+5 a \,b^{2} c -b^{4}-2 \sqrt{-4 a^{3} c^{3}+9 a^{2} b^{2} c^{2}-6 a \,b^{4} c +b^{6}}\, c x -\sqrt{-4 a^{3} c^{3}+9 a^{2} b^{2} c^{2}-6 a \,b^{4} c +b^{6}}\, b \right)}{6 c^{3}}-\frac{\sqrt{-4 a^{3} c^{3}+9 a^{2} b^{2} c^{2}-6 a \,b^{4} c +b^{6}}\, n \ln \left(-4 a^{2} c^{2}+5 a \,b^{2} c -b^{4}+2 \sqrt{-4 a^{3} c^{3}+9 a^{2} b^{2} c^{2}-6 a \,b^{4} c +b^{6}}\, c x +\sqrt{-4 a^{3} c^{3}+9 a^{2} b^{2} c^{2}-6 a \,b^{4} c +b^{6}}\, b \right)}{6 c^{3}}"," ",0,"1/3*x^3*ln((c*x^2+b*x+a)^n)+1/6*I*Pi*x^3*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)^2-1/6*I*Pi*x^3*csgn(I*d)*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)-1/6*I*Pi*x^3*csgn(I*d*(c*x^2+b*x+a)^n)^3+1/6*I*Pi*x^3*csgn(I*d)*csgn(I*d*(c*x^2+b*x+a)^n)^2+1/3*ln(d)*x^3-2/9*n*x^3+1/6*b*n*x^2/c-1/2/c^2*n*ln(-4*a^2*c^2+5*a*b^2*c-b^4+2*(-4*a^3*c^3+9*a^2*b^2*c^2-6*a*b^4*c+b^6)^(1/2)*c*x+(-4*a^3*c^3+9*a^2*b^2*c^2-6*a*b^4*c+b^6)^(1/2)*b)*a*b+1/6/c^3*n*ln(-4*a^2*c^2+5*a*b^2*c-b^4+2*(-4*a^3*c^3+9*a^2*b^2*c^2-6*a*b^4*c+b^6)^(1/2)*c*x+(-4*a^3*c^3+9*a^2*b^2*c^2-6*a*b^4*c+b^6)^(1/2)*b)*b^3-1/2/c^2*n*ln(-4*a^2*c^2+5*a*b^2*c-b^4-2*(-4*a^3*c^3+9*a^2*b^2*c^2-6*a*b^4*c+b^6)^(1/2)*c*x-(-4*a^3*c^3+9*a^2*b^2*c^2-6*a*b^4*c+b^6)^(1/2)*b)*a*b+1/6/c^3*n*ln(-4*a^2*c^2+5*a*b^2*c-b^4-2*(-4*a^3*c^3+9*a^2*b^2*c^2-6*a*b^4*c+b^6)^(1/2)*c*x-(-4*a^3*c^3+9*a^2*b^2*c^2-6*a*b^4*c+b^6)^(1/2)*b)*b^3+2/3/c*a*n*x-1/3*b^2*n*x/c^2-1/6/c^3*n*ln(-4*a^2*c^2+5*a*b^2*c-b^4+2*(-4*a^3*c^3+9*a^2*b^2*c^2-6*a*b^4*c+b^6)^(1/2)*c*x+(-4*a^3*c^3+9*a^2*b^2*c^2-6*a*b^4*c+b^6)^(1/2)*b)*(-4*a^3*c^3+9*a^2*b^2*c^2-6*a*b^4*c+b^6)^(1/2)+1/6/c^3*n*ln(-4*a^2*c^2+5*a*b^2*c-b^4-2*(-4*a^3*c^3+9*a^2*b^2*c^2-6*a*b^4*c+b^6)^(1/2)*c*x-(-4*a^3*c^3+9*a^2*b^2*c^2-6*a*b^4*c+b^6)^(1/2)*b)*(-4*a^3*c^3+9*a^2*b^2*c^2-6*a*b^4*c+b^6)^(1/2)","C"
74,1,510,95,0.680000," ","int(x*ln(d*(c*x^2+b*x+a)^n),x)","-\frac{i \pi  \,x^{2} \mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)}{4}+\frac{i \pi  \,x^{2} \mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}}{4}+\frac{i \pi  \,x^{2} \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}}{4}-\frac{i \pi  \,x^{2} \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{3}}{4}-\frac{n \,x^{2}}{2}+\frac{x^{2} \ln \left(d \right)}{2}+\frac{x^{2} \ln \left(\left(c \,x^{2}+b x +a \right)^{n}\right)}{2}+\frac{a n \ln \left(-4 a b c +b^{3}-2 \sqrt{-4 a \,b^{2} c +b^{4}}\, c x -\sqrt{-4 a \,b^{2} c +b^{4}}\, b \right)}{2 c}+\frac{a n \ln \left(-4 a b c +b^{3}+2 \sqrt{-4 a \,b^{2} c +b^{4}}\, c x +\sqrt{-4 a \,b^{2} c +b^{4}}\, b \right)}{2 c}-\frac{b^{2} n \ln \left(-4 a b c +b^{3}-2 \sqrt{-4 a \,b^{2} c +b^{4}}\, c x -\sqrt{-4 a \,b^{2} c +b^{4}}\, b \right)}{4 c^{2}}-\frac{b^{2} n \ln \left(-4 a b c +b^{3}+2 \sqrt{-4 a \,b^{2} c +b^{4}}\, c x +\sqrt{-4 a \,b^{2} c +b^{4}}\, b \right)}{4 c^{2}}+\frac{b n x}{2 c}+\frac{\sqrt{-4 a \,b^{2} c +b^{4}}\, n \ln \left(-4 a b c +b^{3}-2 \sqrt{-4 a \,b^{2} c +b^{4}}\, c x -\sqrt{-4 a \,b^{2} c +b^{4}}\, b \right)}{4 c^{2}}-\frac{\sqrt{-4 a \,b^{2} c +b^{4}}\, n \ln \left(-4 a b c +b^{3}+2 \sqrt{-4 a \,b^{2} c +b^{4}}\, c x +\sqrt{-4 a \,b^{2} c +b^{4}}\, b \right)}{4 c^{2}}"," ",0,"1/2*x^2*ln((c*x^2+b*x+a)^n)-1/4*I*Pi*x^2*csgn(I*d)*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)+1/4*I*csgn(I*d*(c*x^2+b*x+a)^n)^2*csgn(I*d)*x^2*Pi+1/4*I*csgn(I*d*(c*x^2+b*x+a)^n)^2*csgn(I*(c*x^2+b*x+a)^n)*x^2*Pi-1/4*I*Pi*x^2*csgn(I*d*(c*x^2+b*x+a)^n)^3+1/2*ln(d)*x^2-1/2*n*x^2+1/2/c*n*ln(-2*(-4*a*b^2*c+b^4)^(1/2)*c*x-4*a*b*c+b^3-(-4*a*b^2*c+b^4)^(1/2)*b)*a-1/4/c^2*n*ln(-2*(-4*a*b^2*c+b^4)^(1/2)*c*x-4*a*b*c+b^3-(-4*a*b^2*c+b^4)^(1/2)*b)*b^2+1/2/c*n*ln(2*(-4*a*b^2*c+b^4)^(1/2)*c*x-4*a*b*c+b^3+(-4*a*b^2*c+b^4)^(1/2)*b)*a-1/4/c^2*n*ln(2*(-4*a*b^2*c+b^4)^(1/2)*c*x-4*a*b*c+b^3+(-4*a*b^2*c+b^4)^(1/2)*b)*b^2+1/2*b*n*x/c+1/4/c^2*n*ln(-2*(-4*a*b^2*c+b^4)^(1/2)*c*x-4*a*b*c+b^3-(-4*a*b^2*c+b^4)^(1/2)*b)*(-4*a*b^2*c+b^4)^(1/2)-1/4/c^2*n*ln(2*(-4*a*b^2*c+b^4)^(1/2)*c*x-4*a*b*c+b^3+(-4*a*b^2*c+b^4)^(1/2)*b)*(-4*a*b^2*c+b^4)^(1/2)","C"
75,1,118,73,0.078000," ","int(ln(d*(c*x^2+b*x+a)^n),x)","\frac{4 a n \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-\frac{b^{2} n \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}+\frac{b n \ln \left(c \,x^{2}+b x +a \right)}{2 c}-2 n x +x \ln \left(d \left(c \,x^{2}+b x +a \right)^{n}\right)"," ",0,"x*ln(d*(c*x^2+b*x+a)^n)-2*n*x+1/2*b*n*ln(c*x^2+b*x+a)/c+4*n/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a-n/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2/c","A"
76,1,315,121,0.341000," ","int(ln(d*(c*x^2+b*x+a)^n)/x,x)","-\frac{i \pi  \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right) \ln \left(x \right)}{2}+\frac{i \pi  \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2} \ln \left(x \right)}{2}+\frac{i \pi  \,\mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2} \ln \left(x \right)}{2}-\frac{i \pi  \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{3} \ln \left(x \right)}{2}-n \ln \left(x \right) \ln \left(\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{-b +\sqrt{-4 a c +b^{2}}}\right)-n \ln \left(x \right) \ln \left(\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}\right)-n \dilog \left(\frac{-2 c x -b +\sqrt{-4 a c +b^{2}}}{-b +\sqrt{-4 a c +b^{2}}}\right)-n \dilog \left(\frac{2 c x +b +\sqrt{-4 a c +b^{2}}}{b +\sqrt{-4 a c +b^{2}}}\right)+\ln \left(d \right) \ln \left(x \right)+\ln \left(x \right) \ln \left(\left(c \,x^{2}+b x +a \right)^{n}\right)"," ",0,"ln(x)*ln((c*x^2+b*x+a)^n)-ln(x)*ln((-b-2*c*x+(-4*a*c+b^2)^(1/2))/(-b+(-4*a*c+b^2)^(1/2)))*n-ln(x)*ln((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))*n-dilog((-b-2*c*x+(-4*a*c+b^2)^(1/2))/(-b+(-4*a*c+b^2)^(1/2)))*n-dilog((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b+(-4*a*c+b^2)^(1/2)))*n-1/2*I*ln(x)*Pi*csgn(I*d)*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)+1/2*I*ln(x)*Pi*csgn(I*d)*csgn(I*d*(c*x^2+b*x+a)^n)^2+1/2*I*ln(x)*Pi*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)^2-1/2*I*ln(x)*Pi*csgn(I*d*(c*x^2+b*x+a)^n)^3+ln(x)*ln(d)","C"
77,1,261,80,0.684000," ","int(ln(d*(c*x^2+b*x+a)^n)/x^2,x)","-\frac{\ln \left(\left(c \,x^{2}+b x +a \right)^{n}\right)}{x}-\frac{-i \pi  a \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)+i \pi  a \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}+i \pi  a \,\mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}-i \pi  a \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{3}-2 b n x \ln \left(x \right)-2 a x \RootOf \left(a \,\textit{\_Z}^{2}+b n \textit{\_Z} +c \,n^{2}\right) \ln \left(-\RootOf \left(a \,\textit{\_Z}^{2}+b n \textit{\_Z} +c \,n^{2}\right)^{2} a b +2 b c \,n^{2}+\left(-2 a c n +b^{2} n \right) \RootOf \left(a \,\textit{\_Z}^{2}+b n \textit{\_Z} +c \,n^{2}\right)+\left(\RootOf \left(a \,\textit{\_Z}^{2}+b n \textit{\_Z} +c \,n^{2}\right) b c n +4 c^{2} n^{2}+\left(6 a c -2 b^{2}\right) \RootOf \left(a \,\textit{\_Z}^{2}+b n \textit{\_Z} +c \,n^{2}\right)^{2}\right) x \right)+2 a \ln \left(d \right)}{2 a x}"," ",0,"-1/x*ln((c*x^2+b*x+a)^n)-1/2*(-I*Pi*a*csgn(I*d)*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)+I*Pi*a*csgn(I*d)*csgn(I*d*(c*x^2+b*x+a)^n)^2+I*Pi*a*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)^2-I*Pi*a*csgn(I*d*(c*x^2+b*x+a)^n)^3-2*b*n*ln(x)*x-2*sum(_R*ln(((6*a*c-2*b^2)*_R^2+_R*b*c*n+4*c^2*n^2)*x-a*b*_R^2+(-2*a*c*n+b^2*n)*_R+2*b*c*n^2),_R=RootOf(_Z^2*a+_Z*b*n+c*n^2))*a*x+2*ln(d)*a)/a/x","C"
78,1,1178,107,0.460000," ","int(ln(d*(c*x^2+b*x+a)^n)/x^3,x)","-\frac{\ln \left(\left(c \,x^{2}+b x +a \right)^{n}\right)}{2 x^{2}}-\frac{-4 a c n \,x^{2} \ln \left(x \right)+2 a c n \,x^{2} \ln \left(-12 a^{3} b \,c^{2}+11 a^{2} b^{3} c -2 a \,b^{5}+5 \sqrt{-4 a \,b^{2} c +b^{4}}\, a^{2} b c -2 \sqrt{-4 a \,b^{2} c +b^{4}}\, a \,b^{3}+\left(-16 a^{2} b^{2} c^{2}+12 a \,b^{4} c -2 b^{6}-6 \sqrt{-4 a \,b^{2} c +b^{4}}\, a^{2} c^{2}+8 \sqrt{-4 a \,b^{2} c +b^{4}}\, a \,b^{2} c -2 \sqrt{-4 a \,b^{2} c +b^{4}}\, b^{4}\right) x \right)+2 a c n \,x^{2} \ln \left(-12 a^{3} b \,c^{2}+11 a^{2} b^{3} c -2 a \,b^{5}-5 \sqrt{-4 a \,b^{2} c +b^{4}}\, a^{2} b c +2 \sqrt{-4 a \,b^{2} c +b^{4}}\, a \,b^{3}+\left(-16 a^{2} b^{2} c^{2}+12 a \,b^{4} c -2 b^{6}+6 \sqrt{-4 a \,b^{2} c +b^{4}}\, a^{2} c^{2}-8 \sqrt{-4 a \,b^{2} c +b^{4}}\, a \,b^{2} c +2 \sqrt{-4 a \,b^{2} c +b^{4}}\, b^{4}\right) x \right)+2 b^{2} n \,x^{2} \ln \left(x \right)-b^{2} n \,x^{2} \ln \left(-12 a^{3} b \,c^{2}+11 a^{2} b^{3} c -2 a \,b^{5}+5 \sqrt{-4 a \,b^{2} c +b^{4}}\, a^{2} b c -2 \sqrt{-4 a \,b^{2} c +b^{4}}\, a \,b^{3}+\left(-16 a^{2} b^{2} c^{2}+12 a \,b^{4} c -2 b^{6}-6 \sqrt{-4 a \,b^{2} c +b^{4}}\, a^{2} c^{2}+8 \sqrt{-4 a \,b^{2} c +b^{4}}\, a \,b^{2} c -2 \sqrt{-4 a \,b^{2} c +b^{4}}\, b^{4}\right) x \right)-b^{2} n \,x^{2} \ln \left(-12 a^{3} b \,c^{2}+11 a^{2} b^{3} c -2 a \,b^{5}-5 \sqrt{-4 a \,b^{2} c +b^{4}}\, a^{2} b c +2 \sqrt{-4 a \,b^{2} c +b^{4}}\, a \,b^{3}+\left(-16 a^{2} b^{2} c^{2}+12 a \,b^{4} c -2 b^{6}+6 \sqrt{-4 a \,b^{2} c +b^{4}}\, a^{2} c^{2}-8 \sqrt{-4 a \,b^{2} c +b^{4}}\, a \,b^{2} c +2 \sqrt{-4 a \,b^{2} c +b^{4}}\, b^{4}\right) x \right)-i \pi  \,a^{2} \mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)+i \pi  \,a^{2} \mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}+i \pi  \,a^{2} \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}-i \pi  \,a^{2} \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{3}+2 a b n x -\sqrt{-4 a \,b^{2} c +b^{4}}\, n \,x^{2} \ln \left(-12 a^{3} b \,c^{2}+11 a^{2} b^{3} c -2 a \,b^{5}+5 \sqrt{-4 a \,b^{2} c +b^{4}}\, a^{2} b c -2 \sqrt{-4 a \,b^{2} c +b^{4}}\, a \,b^{3}+\left(-16 a^{2} b^{2} c^{2}+12 a \,b^{4} c -2 b^{6}-6 \sqrt{-4 a \,b^{2} c +b^{4}}\, a^{2} c^{2}+8 \sqrt{-4 a \,b^{2} c +b^{4}}\, a \,b^{2} c -2 \sqrt{-4 a \,b^{2} c +b^{4}}\, b^{4}\right) x \right)+\sqrt{-4 a \,b^{2} c +b^{4}}\, n \,x^{2} \ln \left(-12 a^{3} b \,c^{2}+11 a^{2} b^{3} c -2 a \,b^{5}-5 \sqrt{-4 a \,b^{2} c +b^{4}}\, a^{2} b c +2 \sqrt{-4 a \,b^{2} c +b^{4}}\, a \,b^{3}+\left(-16 a^{2} b^{2} c^{2}+12 a \,b^{4} c -2 b^{6}+6 \sqrt{-4 a \,b^{2} c +b^{4}}\, a^{2} c^{2}-8 \sqrt{-4 a \,b^{2} c +b^{4}}\, a \,b^{2} c +2 \sqrt{-4 a \,b^{2} c +b^{4}}\, b^{4}\right) x \right)+2 a^{2} \ln \left(d \right)}{4 a^{2} x^{2}}"," ",0,"-1/2/x^2*ln((c*x^2+b*x+a)^n)-1/4*(-I*Pi*a^2*csgn(I*d)*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)+I*Pi*a^2*csgn(I*d)*csgn(I*d*(c*x^2+b*x+a)^n)^2+I*Pi*a^2*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)^2-I*Pi*a^2*csgn(I*d*(c*x^2+b*x+a)^n)^3+2*n*ln((-16*a^2*b^2*c^2+12*a*b^4*c-2*b^6-6*(-4*a*b^2*c+b^4)^(1/2)*a^2*c^2+8*(-4*a*b^2*c+b^4)^(1/2)*a*b^2*c-2*(-4*a*b^2*c+b^4)^(1/2)*b^4)*x-12*a^3*b*c^2+11*a^2*b^3*c-2*a*b^5+5*(-4*a*b^2*c+b^4)^(1/2)*a^2*b*c-2*(-4*a*b^2*c+b^4)^(1/2)*a*b^3)*c*a*x^2-n*ln((-16*a^2*b^2*c^2+12*a*b^4*c-2*b^6-6*(-4*a*b^2*c+b^4)^(1/2)*a^2*c^2+8*(-4*a*b^2*c+b^4)^(1/2)*a*b^2*c-2*(-4*a*b^2*c+b^4)^(1/2)*b^4)*x-12*a^3*b*c^2+11*a^2*b^3*c-2*a*b^5+5*(-4*a*b^2*c+b^4)^(1/2)*a^2*b*c-2*(-4*a*b^2*c+b^4)^(1/2)*a*b^3)*b^2*x^2+2*n*ln((-16*a^2*b^2*c^2+12*a*b^4*c-2*b^6+6*(-4*a*b^2*c+b^4)^(1/2)*a^2*c^2-8*(-4*a*b^2*c+b^4)^(1/2)*a*b^2*c+2*(-4*a*b^2*c+b^4)^(1/2)*b^4)*x-12*a^3*b*c^2+11*a^2*b^3*c-2*a*b^5-5*(-4*a*b^2*c+b^4)^(1/2)*a^2*b*c+2*(-4*a*b^2*c+b^4)^(1/2)*a*b^3)*c*a*x^2-n*ln((-16*a^2*b^2*c^2+12*a*b^4*c-2*b^6+6*(-4*a*b^2*c+b^4)^(1/2)*a^2*c^2-8*(-4*a*b^2*c+b^4)^(1/2)*a*b^2*c+2*(-4*a*b^2*c+b^4)^(1/2)*b^4)*x-12*a^3*b*c^2+11*a^2*b^3*c-2*a*b^5-5*(-4*a*b^2*c+b^4)^(1/2)*a^2*b*c+2*(-4*a*b^2*c+b^4)^(1/2)*a*b^3)*b^2*x^2-4*n*ln(x)*c*a*x^2+2*n*ln(x)*b^2*x^2-n*ln((-16*a^2*b^2*c^2+12*a*b^4*c-2*b^6-6*(-4*a*b^2*c+b^4)^(1/2)*a^2*c^2+8*(-4*a*b^2*c+b^4)^(1/2)*a*b^2*c-2*(-4*a*b^2*c+b^4)^(1/2)*b^4)*x-12*a^3*b*c^2+11*a^2*b^3*c-2*a*b^5+5*(-4*a*b^2*c+b^4)^(1/2)*a^2*b*c-2*(-4*a*b^2*c+b^4)^(1/2)*a*b^3)*(-4*a*b^2*c+b^4)^(1/2)*x^2+n*ln((-16*a^2*b^2*c^2+12*a*b^4*c-2*b^6+6*(-4*a*b^2*c+b^4)^(1/2)*a^2*c^2-8*(-4*a*b^2*c+b^4)^(1/2)*a*b^2*c+2*(-4*a*b^2*c+b^4)^(1/2)*b^4)*x-12*a^3*b*c^2+11*a^2*b^3*c-2*a*b^5-5*(-4*a*b^2*c+b^4)^(1/2)*a^2*b*c+2*(-4*a*b^2*c+b^4)^(1/2)*a*b^3)*(-4*a*b^2*c+b^4)^(1/2)*x^2+2*a*b*n*x+2*ln(d)*a^2)/a^2/x^2","C"
79,1,423,133,0.714000," ","int(ln(d*(c*x^2+b*x+a)^n)/x^4,x)","-\frac{\ln \left(\left(c \,x^{2}+b x +a \right)^{n}\right)}{3 x^{3}}-\frac{6 a b c n \,x^{3} \ln \left(x \right)-2 b^{3} n \,x^{3} \ln \left(x \right)-2 a^{3} x^{3} \RootOf \left(\textit{\_Z}^{2} a^{3}+c^{3} n^{2}+\left(-3 c b n a +b^{3} n \right) \textit{\_Z} \right) \ln \left(-\RootOf \left(\textit{\_Z}^{2} a^{3}+c^{3} n^{2}+\left(-3 c b n a +b^{3} n \right) \textit{\_Z} \right)^{2} a^{5} b +6 a^{2} b \,c^{3} n^{2}-5 a \,b^{3} c^{2} n^{2}+b^{5} c \,n^{2}+\left(2 a^{4} c^{2} n -4 a^{3} b^{2} c n +a^{2} b^{4} n \right) \RootOf \left(\textit{\_Z}^{2} a^{3}+c^{3} n^{2}+\left(-3 c b n a +b^{3} n \right) \textit{\_Z} \right)+\left(4 a^{2} c^{4} n^{2}-4 a \,b^{2} c^{3} n^{2}+b^{4} c^{2} n^{2}+\left(6 a^{5} c -2 a^{4} b^{2}\right) \RootOf \left(\textit{\_Z}^{2} a^{3}+c^{3} n^{2}+\left(-3 c b n a +b^{3} n \right) \textit{\_Z} \right)^{2}+\left(-7 a^{3} b \,c^{2} n +2 a^{2} b^{3} c n \right) \RootOf \left(\textit{\_Z}^{2} a^{3}+c^{3} n^{2}+\left(-3 c b n a +b^{3} n \right) \textit{\_Z} \right)\right) x \right)-i \pi  \,a^{3} \mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)+i \pi  \,a^{3} \mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}+i \pi  \,a^{3} \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}-i \pi  \,a^{3} \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{3}+4 a^{2} c n \,x^{2}-2 a \,b^{2} n \,x^{2}+a^{2} b n x +2 a^{3} \ln \left(d \right)}{6 a^{3} x^{3}}"," ",0,"-1/3/x^3*ln((c*x^2+b*x+a)^n)-1/6*(-I*Pi*a^3*csgn(I*d)*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)+I*Pi*a^3*csgn(I*d)*csgn(I*d*(c*x^2+b*x+a)^n)^2+I*Pi*a^3*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)^2-I*Pi*a^3*csgn(I*d*(c*x^2+b*x+a)^n)^3+6*ln(x)*a*b*c*n*x^3-2*ln(x)*b^3*n*x^3-2*sum(_R*ln(((6*a^5*c-2*a^4*b^2)*_R^2+(-7*a^3*b*c^2*n+2*a^2*b^3*c*n)*_R+4*a^2*c^4*n^2-4*a*b^2*c^3*n^2+b^4*c^2*n^2)*x-a^5*b*_R^2+(2*a^4*c^2*n-4*a^3*b^2*c*n+a^2*b^4*n)*_R+6*a^2*b*c^3*n^2-5*a*b^3*c^2*n^2+b^5*c*n^2),_R=RootOf(a^3*_Z^2+(-3*a*b*c*n+b^3*n)*_Z+c^3*n^2))*a^3*x^3+4*a^2*c*n*x^2-2*a*b^2*n*x^2+a^2*b*n*x+2*ln(d)*a^3)/a^3/x^3","C"
80,1,505,172,0.878000," ","int(ln(d*(c*x^2+b*x+a)^n)/x^5,x)","-\frac{\ln \left(\left(c \,x^{2}+b x +a \right)^{n}\right)}{4 x^{4}}-\frac{12 a^{2} c^{2} n \,x^{4} \ln \left(x \right)-24 a \,b^{2} c n \,x^{4} \ln \left(x \right)+6 b^{4} n \,x^{4} \ln \left(x \right)-6 a^{4} x^{4} \RootOf \left(\textit{\_Z}^{2} a^{4}+c^{4} n^{2}+\left(-2 a^{2} c^{2} n +4 a \,b^{2} c n -b^{4} n \right) \textit{\_Z} \right) \ln \left(-\RootOf \left(\textit{\_Z}^{2} a^{4}+c^{4} n^{2}+\left(-2 a^{2} c^{2} n +4 a \,b^{2} c n -b^{4} n \right) \textit{\_Z} \right)^{2} a^{7} b -6 a^{3} b \,c^{4} n^{2}+14 a^{2} b^{3} c^{3} n^{2}-7 a \,b^{5} c^{2} n^{2}+b^{7} c \,n^{2}+\left(-5 a^{5} b \,c^{2} n +5 a^{4} b^{3} c n -a^{3} b^{5} n \right) \RootOf \left(\textit{\_Z}^{2} a^{4}+c^{4} n^{2}+\left(-2 a^{2} c^{2} n +4 a \,b^{2} c n -b^{4} n \right) \textit{\_Z} \right)+\left(9 a^{2} b^{2} c^{4} n^{2}-6 a \,b^{4} c^{3} n^{2}+b^{6} c^{2} n^{2}+\left(6 a^{7} c -2 a^{6} b^{2}\right) \RootOf \left(\textit{\_Z}^{2} a^{4}+c^{4} n^{2}+\left(-2 a^{2} c^{2} n +4 a \,b^{2} c n -b^{4} n \right) \textit{\_Z} \right)^{2}+\left(-6 a^{5} c^{3} n +9 a^{4} b^{2} c^{2} n -2 a^{3} b^{4} c n \right) \RootOf \left(\textit{\_Z}^{2} a^{4}+c^{4} n^{2}+\left(-2 a^{2} c^{2} n +4 a \,b^{2} c n -b^{4} n \right) \textit{\_Z} \right)\right) x \right)-18 a^{2} b c n \,x^{3}+6 a \,b^{3} n \,x^{3}-3 i \pi  \,a^{4} \mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)+3 i \pi  \,a^{4} \mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}+3 i \pi  \,a^{4} \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}-3 i \pi  \,a^{4} \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{3}+6 a^{3} c n \,x^{2}-3 a^{2} b^{2} n \,x^{2}+2 a^{3} b n x +6 a^{4} \ln \left(d \right)}{24 a^{4} x^{4}}"," ",0,"-1/4/x^4*ln((c*x^2+b*x+a)^n)-1/24*(12*ln(x)*a^2*c^2*n*x^4-24*ln(x)*a*b^2*c*n*x^4+6*ln(x)*b^4*n*x^4-3*I*Pi*a^4*csgn(I*d)*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)+3*I*Pi*a^4*csgn(I*d)*csgn(I*d*(c*x^2+b*x+a)^n)^2+3*I*Pi*a^4*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)^2-3*I*Pi*a^4*csgn(I*d*(c*x^2+b*x+a)^n)^3-6*sum(_R*ln(((6*a^7*c-2*a^6*b^2)*_R^2+(-6*a^5*c^3*n+9*a^4*b^2*c^2*n-2*a^3*b^4*c*n)*_R+9*a^2*b^2*c^4*n^2-6*a*b^4*c^3*n^2+b^6*c^2*n^2)*x-a^7*b*_R^2+(-5*a^5*b*c^2*n+5*a^4*b^3*c*n-a^3*b^5*n)*_R-6*a^3*b*c^4*n^2+14*a^2*b^3*c^3*n^2-7*a*b^5*c^2*n^2+b^7*c*n^2),_R=RootOf(a^4*_Z^2+(-2*a^2*c^2*n+4*a*b^2*c*n-b^4*n)*_Z+c^4*n^2))*a^4*x^4-18*a^2*b*c*n*x^3+6*a*b^3*n*x^3+6*a^3*c*n*x^2-3*a^2*b^2*n*x^2+2*a^3*b*n*x+6*ln(d)*a^4)/a^4/x^4","C"
81,1,38,37,0.069000," ","int(ln(x^2+x+1),x)","x \ln \left(x^{2}+x +1\right)-2 x +\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)+\frac{\ln \left(x^{2}+x +1\right)}{2}"," ",0,"-2*x+1/2*ln(x^2+x+1)+x*ln(x^2+x+1)+3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))","A"
82,1,31895,465,1.088000," ","int((e*x+d)^4*ln(d*(c*x^2+b*x+a)^n),x)","\text{output too large to display}"," ",0,"result too large to display","C"
83,1,16059,320,0.873000," ","int((e*x+d)^3*ln(d*(c*x^2+b*x+a)^n),x)","\text{output too large to display}"," ",0,"result too large to display","C"
84,1,7155,210,0.700000," ","int((e*x+d)^2*ln(d*(c*x^2+b*x+a)^n),x)","\text{output too large to display}"," ",0,"result too large to display","C"
85,1,1706,140,0.695000," ","int((e*x+d)*ln(d*(c*x^2+b*x+a)^n),x)","-\frac{i \pi  e \,x^{2} \mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)}{4}+\frac{i \pi  e \,x^{2} \mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}}{4}+\frac{i \pi  e \,x^{2} \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}}{4}-\frac{i \pi  e \,x^{2} \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{3}}{4}-\frac{i \pi  d x \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)}{2}+\frac{i \pi  d x \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}}{2}+\frac{i \pi  d x \,\mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}}{2}-\frac{i \pi  d x \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{3}}{2}-\frac{e n \,x^{2}}{2}+\frac{e \,x^{2} \ln \left(d \right)}{2}+\frac{a e n \ln \left(-4 a b c e +8 a \,c^{2} d +b^{3} e -2 b^{2} c d -2 \sqrt{-4 a \,b^{2} c \,e^{2}+16 a b \,c^{2} d e -16 a \,c^{3} d^{2}+b^{4} e^{2}-4 b^{3} c d e +4 b^{2} c^{2} d^{2}}\, c x -\sqrt{-4 a \,b^{2} c \,e^{2}+16 a b \,c^{2} d e -16 a \,c^{3} d^{2}+b^{4} e^{2}-4 b^{3} c d e +4 b^{2} c^{2} d^{2}}\, b \right)}{2 c}+\frac{a e n \ln \left(-4 a b c e +8 a \,c^{2} d +b^{3} e -2 b^{2} c d +2 \sqrt{-4 a \,b^{2} c \,e^{2}+16 a b \,c^{2} d e -16 a \,c^{3} d^{2}+b^{4} e^{2}-4 b^{3} c d e +4 b^{2} c^{2} d^{2}}\, c x +\sqrt{-4 a \,b^{2} c \,e^{2}+16 a b \,c^{2} d e -16 a \,c^{3} d^{2}+b^{4} e^{2}-4 b^{3} c d e +4 b^{2} c^{2} d^{2}}\, b \right)}{2 c}-\frac{b^{2} e n \ln \left(-4 a b c e +8 a \,c^{2} d +b^{3} e -2 b^{2} c d -2 \sqrt{-4 a \,b^{2} c \,e^{2}+16 a b \,c^{2} d e -16 a \,c^{3} d^{2}+b^{4} e^{2}-4 b^{3} c d e +4 b^{2} c^{2} d^{2}}\, c x -\sqrt{-4 a \,b^{2} c \,e^{2}+16 a b \,c^{2} d e -16 a \,c^{3} d^{2}+b^{4} e^{2}-4 b^{3} c d e +4 b^{2} c^{2} d^{2}}\, b \right)}{4 c^{2}}-\frac{b^{2} e n \ln \left(-4 a b c e +8 a \,c^{2} d +b^{3} e -2 b^{2} c d +2 \sqrt{-4 a \,b^{2} c \,e^{2}+16 a b \,c^{2} d e -16 a \,c^{3} d^{2}+b^{4} e^{2}-4 b^{3} c d e +4 b^{2} c^{2} d^{2}}\, c x +\sqrt{-4 a \,b^{2} c \,e^{2}+16 a b \,c^{2} d e -16 a \,c^{3} d^{2}+b^{4} e^{2}-4 b^{3} c d e +4 b^{2} c^{2} d^{2}}\, b \right)}{4 c^{2}}+\frac{b d n \ln \left(-4 a b c e +8 a \,c^{2} d +b^{3} e -2 b^{2} c d -2 \sqrt{-4 a \,b^{2} c \,e^{2}+16 a b \,c^{2} d e -16 a \,c^{3} d^{2}+b^{4} e^{2}-4 b^{3} c d e +4 b^{2} c^{2} d^{2}}\, c x -\sqrt{-4 a \,b^{2} c \,e^{2}+16 a b \,c^{2} d e -16 a \,c^{3} d^{2}+b^{4} e^{2}-4 b^{3} c d e +4 b^{2} c^{2} d^{2}}\, b \right)}{2 c}+\frac{b d n \ln \left(-4 a b c e +8 a \,c^{2} d +b^{3} e -2 b^{2} c d +2 \sqrt{-4 a \,b^{2} c \,e^{2}+16 a b \,c^{2} d e -16 a \,c^{3} d^{2}+b^{4} e^{2}-4 b^{3} c d e +4 b^{2} c^{2} d^{2}}\, c x +\sqrt{-4 a \,b^{2} c \,e^{2}+16 a b \,c^{2} d e -16 a \,c^{3} d^{2}+b^{4} e^{2}-4 b^{3} c d e +4 b^{2} c^{2} d^{2}}\, b \right)}{2 c}+\frac{b e n x}{2 c}-2 d n x +d x \ln \left(d \right)+\left(\frac{1}{2} e \,x^{2}+d x \right) \ln \left(\left(c \,x^{2}+b x +a \right)^{n}\right)+\frac{\sqrt{-4 a \,b^{2} c \,e^{2}+16 a b \,c^{2} d e -16 a \,c^{3} d^{2}+b^{4} e^{2}-4 b^{3} c d e +4 b^{2} c^{2} d^{2}}\, n \ln \left(-4 a b c e +8 a \,c^{2} d +b^{3} e -2 b^{2} c d -2 \sqrt{-4 a \,b^{2} c \,e^{2}+16 a b \,c^{2} d e -16 a \,c^{3} d^{2}+b^{4} e^{2}-4 b^{3} c d e +4 b^{2} c^{2} d^{2}}\, c x -\sqrt{-4 a \,b^{2} c \,e^{2}+16 a b \,c^{2} d e -16 a \,c^{3} d^{2}+b^{4} e^{2}-4 b^{3} c d e +4 b^{2} c^{2} d^{2}}\, b \right)}{4 c^{2}}-\frac{\sqrt{-4 a \,b^{2} c \,e^{2}+16 a b \,c^{2} d e -16 a \,c^{3} d^{2}+b^{4} e^{2}-4 b^{3} c d e +4 b^{2} c^{2} d^{2}}\, n \ln \left(-4 a b c e +8 a \,c^{2} d +b^{3} e -2 b^{2} c d +2 \sqrt{-4 a \,b^{2} c \,e^{2}+16 a b \,c^{2} d e -16 a \,c^{3} d^{2}+b^{4} e^{2}-4 b^{3} c d e +4 b^{2} c^{2} d^{2}}\, c x +\sqrt{-4 a \,b^{2} c \,e^{2}+16 a b \,c^{2} d e -16 a \,c^{3} d^{2}+b^{4} e^{2}-4 b^{3} c d e +4 b^{2} c^{2} d^{2}}\, b \right)}{4 c^{2}}"," ",0,"(1/2*e*x^2+d*x)*ln((c*x^2+b*x+a)^n)-1/4*I*Pi*e*x^2*csgn(I*d*(c*x^2+b*x+a)^n)^3-1/2*I*Pi*d*x*csgn(I*d)*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)+1/2*I*Pi*d*x*csgn(I*d)*csgn(I*d*(c*x^2+b*x+a)^n)^2+1/4*I*csgn(I*d*(c*x^2+b*x+a)^n)^2*csgn(I*d)*x^2*e*Pi-1/4*I*Pi*e*x^2*csgn(I*d)*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)+1/4*I*csgn(I*d*(c*x^2+b*x+a)^n)^2*csgn(I*(c*x^2+b*x+a)^n)*x^2*e*Pi-1/2*I*Pi*d*x*csgn(I*d*(c*x^2+b*x+a)^n)^3+1/2*I*Pi*d*x*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)^2+1/2*ln(d)*e*x^2-1/2*e*n*x^2+ln(d)*d*x+1/2/c*n*ln(-4*a*b*c*e+8*a*c^2*d+b^3*e-2*b^2*c*d-2*(-4*a*b^2*c*e^2+16*a*b*c^2*d*e-16*a*c^3*d^2+b^4*e^2-4*b^3*c*d*e+4*b^2*c^2*d^2)^(1/2)*c*x-(-4*a*b^2*c*e^2+16*a*b*c^2*d*e-16*a*c^3*d^2+b^4*e^2-4*b^3*c*d*e+4*b^2*c^2*d^2)^(1/2)*b)*a*e-1/4/c^2*n*ln(-4*a*b*c*e+8*a*c^2*d+b^3*e-2*b^2*c*d-2*(-4*a*b^2*c*e^2+16*a*b*c^2*d*e-16*a*c^3*d^2+b^4*e^2-4*b^3*c*d*e+4*b^2*c^2*d^2)^(1/2)*c*x-(-4*a*b^2*c*e^2+16*a*b*c^2*d*e-16*a*c^3*d^2+b^4*e^2-4*b^3*c*d*e+4*b^2*c^2*d^2)^(1/2)*b)*b^2*e+1/2/c*n*ln(-4*a*b*c*e+8*a*c^2*d+b^3*e-2*b^2*c*d-2*(-4*a*b^2*c*e^2+16*a*b*c^2*d*e-16*a*c^3*d^2+b^4*e^2-4*b^3*c*d*e+4*b^2*c^2*d^2)^(1/2)*c*x-(-4*a*b^2*c*e^2+16*a*b*c^2*d*e-16*a*c^3*d^2+b^4*e^2-4*b^3*c*d*e+4*b^2*c^2*d^2)^(1/2)*b)*b*d+1/2/c*n*ln(-4*a*b*c*e+8*a*c^2*d+b^3*e-2*b^2*c*d+2*(-4*a*b^2*c*e^2+16*a*b*c^2*d*e-16*a*c^3*d^2+b^4*e^2-4*b^3*c*d*e+4*b^2*c^2*d^2)^(1/2)*c*x+(-4*a*b^2*c*e^2+16*a*b*c^2*d*e-16*a*c^3*d^2+b^4*e^2-4*b^3*c*d*e+4*b^2*c^2*d^2)^(1/2)*b)*a*e-1/4/c^2*n*ln(-4*a*b*c*e+8*a*c^2*d+b^3*e-2*b^2*c*d+2*(-4*a*b^2*c*e^2+16*a*b*c^2*d*e-16*a*c^3*d^2+b^4*e^2-4*b^3*c*d*e+4*b^2*c^2*d^2)^(1/2)*c*x+(-4*a*b^2*c*e^2+16*a*b*c^2*d*e-16*a*c^3*d^2+b^4*e^2-4*b^3*c*d*e+4*b^2*c^2*d^2)^(1/2)*b)*b^2*e+1/2/c*n*ln(-4*a*b*c*e+8*a*c^2*d+b^3*e-2*b^2*c*d+2*(-4*a*b^2*c*e^2+16*a*b*c^2*d*e-16*a*c^3*d^2+b^4*e^2-4*b^3*c*d*e+4*b^2*c^2*d^2)^(1/2)*c*x+(-4*a*b^2*c*e^2+16*a*b*c^2*d*e-16*a*c^3*d^2+b^4*e^2-4*b^3*c*d*e+4*b^2*c^2*d^2)^(1/2)*b)*b*d+1/2/c*b*e*n*x-2*d*n*x+1/4/c^2*n*ln(-4*a*b*c*e+8*a*c^2*d+b^3*e-2*b^2*c*d-2*(-4*a*b^2*c*e^2+16*a*b*c^2*d*e-16*a*c^3*d^2+b^4*e^2-4*b^3*c*d*e+4*b^2*c^2*d^2)^(1/2)*c*x-(-4*a*b^2*c*e^2+16*a*b*c^2*d*e-16*a*c^3*d^2+b^4*e^2-4*b^3*c*d*e+4*b^2*c^2*d^2)^(1/2)*b)*(-4*a*b^2*c*e^2+16*a*b*c^2*d*e-16*a*c^3*d^2+b^4*e^2-4*b^3*c*d*e+4*b^2*c^2*d^2)^(1/2)-1/4/c^2*n*ln(-4*a*b*c*e+8*a*c^2*d+b^3*e-2*b^2*c*d+2*(-4*a*b^2*c*e^2+16*a*b*c^2*d*e-16*a*c^3*d^2+b^4*e^2-4*b^3*c*d*e+4*b^2*c^2*d^2)^(1/2)*c*x+(-4*a*b^2*c*e^2+16*a*b*c^2*d*e-16*a*c^3*d^2+b^4*e^2-4*b^3*c*d*e+4*b^2*c^2*d^2)^(1/2)*b)*(-4*a*b^2*c*e^2+16*a*b*c^2*d*e-16*a*c^3*d^2+b^4*e^2-4*b^3*c*d*e+4*b^2*c^2*d^2)^(1/2)","C"
86,1,118,73,0.076000," ","int(ln(d*(c*x^2+b*x+a)^n),x)","\frac{4 a n \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-\frac{b^{2} n \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}+\frac{b n \ln \left(c \,x^{2}+b x +a \right)}{2 c}-2 n x +x \ln \left(d \left(c \,x^{2}+b x +a \right)^{n}\right)"," ",0,"4/(4*a*c-b^2)^(1/2)*a*n*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))-1/(4*a*c-b^2)^(1/2)*b^2/c*n*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))+1/2*b/c*n*ln(c*x^2+b*x+a)-2*n*x+x*ln(d*(c*x^2+b*x+a)^n)","A"
87,1,493,216,0.369000," ","int(ln(d*(c*x^2+b*x+a)^n)/(e*x+d),x)","-\frac{i \pi  \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right) \ln \left(e x +d \right)}{2 e}+\frac{i \pi  \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2} \ln \left(e x +d \right)}{2 e}+\frac{i \pi  \,\mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2} \ln \left(e x +d \right)}{2 e}-\frac{i \pi  \mathrm{csgn}\left(i d \left(c \,x^{2}+b x +a \right)^{n}\right)^{3} \ln \left(e x +d \right)}{2 e}-\frac{n \ln \left(\frac{-b e +2 c d -2 \left(e x +d \right) c +\sqrt{-4 c \,e^{2} a +b^{2} e^{2}}}{-b e +2 c d +\sqrt{-4 c \,e^{2} a +b^{2} e^{2}}}\right) \ln \left(e x +d \right)}{e}-\frac{n \ln \left(\frac{b e -2 c d +2 \left(e x +d \right) c +\sqrt{-4 c \,e^{2} a +b^{2} e^{2}}}{b e -2 c d +\sqrt{-4 c \,e^{2} a +b^{2} e^{2}}}\right) \ln \left(e x +d \right)}{e}-\frac{n \dilog \left(\frac{-b e +2 c d -2 \left(e x +d \right) c +\sqrt{-4 c \,e^{2} a +b^{2} e^{2}}}{-b e +2 c d +\sqrt{-4 c \,e^{2} a +b^{2} e^{2}}}\right)}{e}-\frac{n \dilog \left(\frac{b e -2 c d +2 \left(e x +d \right) c +\sqrt{-4 c \,e^{2} a +b^{2} e^{2}}}{b e -2 c d +\sqrt{-4 c \,e^{2} a +b^{2} e^{2}}}\right)}{e}+\frac{\ln \left(d \right) \ln \left(e x +d \right)}{e}+\frac{\ln \left(\left(c \,x^{2}+b x +a \right)^{n}\right) \ln \left(e x +d \right)}{e}"," ",0,"ln(e*x+d)/e*ln((c*x^2+b*x+a)^n)-1/e*n*ln(e*x+d)*ln((2*(e*x+d)*c+b*e-2*c*d+(-4*a*c*e^2+b^2*e^2)^(1/2))/(b*e-2*c*d+(-4*a*c*e^2+b^2*e^2)^(1/2)))-1/e*n*ln(e*x+d)*ln((-2*(e*x+d)*c-b*e+2*c*d+(-4*a*c*e^2+b^2*e^2)^(1/2))/(-b*e+2*c*d+(-4*a*c*e^2+b^2*e^2)^(1/2)))-1/e*n*dilog((2*(e*x+d)*c+b*e-2*c*d+(-4*a*c*e^2+b^2*e^2)^(1/2))/(b*e-2*c*d+(-4*a*c*e^2+b^2*e^2)^(1/2)))-1/e*n*dilog((-2*(e*x+d)*c-b*e+2*c*d+(-4*a*c*e^2+b^2*e^2)^(1/2))/(-b*e+2*c*d+(-4*a*c*e^2+b^2*e^2)^(1/2)))-1/2*I*ln(e*x+d)/e*Pi*csgn(I*d)*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)+1/2*I*ln(e*x+d)/e*Pi*csgn(I*d)*csgn(I*d*(c*x^2+b*x+a)^n)^2+1/2*I*ln(e*x+d)/e*Pi*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*d*(c*x^2+b*x+a)^n)^2-1/2*I*ln(e*x+d)/e*Pi*csgn(I*d*(c*x^2+b*x+a)^n)^3+ln(e*x+d)/e*ln(d)","C"
88,1,6540,159,0.716000," ","int(ln(d*(c*x^2+b*x+a)^n)/(e*x+d)^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
89,1,14679,245,1.190000," ","int(ln(d*(c*x^2+b*x+a)^n)/(e*x+d)^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
90,1,306209,340,1.038000," ","int(ln(d*(c*x^2+b*x+a)^n)/(e*x+d)^4,x)","\text{output too large to display}"," ",0,"result too large to display","C"
91,1,1137077,501,1.297000," ","int(ln(d*(c*x^2+b*x+a)^n)/(e*x+d)^5,x)","\text{output too large to display}"," ",0,"result too large to display","B"
92,0,0,131,1.046000," ","int(ln(d*(c*x^2+a)^n)/(c*e*x^2+a*e),x)","\int \frac{\ln \left(d \left(c \,x^{2}+a \right)^{n}\right)}{c e \,x^{2}+a e}\, dx"," ",0,"int(ln(d*(c*x^2+a)^n)/(c*e*x^2+a*e),x)","F"
93,0,0,232,1.709000," ","int(ln(d*(c*x^2+b*x+a)^n)/(c*e*x^2+b*e*x+a*e),x)","\int \frac{\ln \left(d \left(c \,x^{2}+b x +a \right)^{n}\right)}{c e \,x^{2}+b e x +a e}\, dx"," ",0,"int(ln(d*(c*x^2+b*x+a)^n)/(c*e*x^2+b*e*x+a*e),x)","F"
94,1,610,598,1.197000," ","int(ln(g*(c*x^2+b*x+a)^n)/(e*x^2+d),x)","-\frac{i \pi  \arctan \left(\frac{e x}{\sqrt{d e}}\right) \mathrm{csgn}\left(i g \right) \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i g \left(c \,x^{2}+b x +a \right)^{n}\right)}{2 \sqrt{d e}}+\frac{i \pi  \arctan \left(\frac{e x}{\sqrt{d e}}\right) \mathrm{csgn}\left(i g \right) \mathrm{csgn}\left(i g \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}}{2 \sqrt{d e}}+\frac{i \pi  \arctan \left(\frac{e x}{\sqrt{d e}}\right) \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i g \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}}{2 \sqrt{d e}}-\frac{i \pi  \arctan \left(\frac{e x}{\sqrt{d e}}\right) \mathrm{csgn}\left(i g \left(c \,x^{2}+b x +a \right)^{n}\right)^{3}}{2 \sqrt{d e}}+\frac{\arctan \left(\frac{e x}{\sqrt{d e}}\right) \ln \left(g \right)}{\sqrt{d e}}+\frac{n \left(-\ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+d \right)-x +\RootOf \left(\textit{\_Z}^{2} c e +\RootOf \left(e \,\textit{\_Z}^{2}+d \right) b e +a e -c d +\left(2 \RootOf \left(e \,\textit{\_Z}^{2}+d \right) c e +b e \right) \textit{\_Z} , \mathit{index} =1\right)}{\RootOf \left(\textit{\_Z}^{2} c e +\RootOf \left(e \,\textit{\_Z}^{2}+d \right) b e +a e -c d +\left(2 \RootOf \left(e \,\textit{\_Z}^{2}+d \right) c e +b e \right) \textit{\_Z} , \mathit{index} =1\right)}\right) \ln \left(-\RootOf \left(e \,\textit{\_Z}^{2}+d \right)+x \right)-\ln \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+d \right)-x +\RootOf \left(\textit{\_Z}^{2} c e +\RootOf \left(e \,\textit{\_Z}^{2}+d \right) b e +a e -c d +\left(2 \RootOf \left(e \,\textit{\_Z}^{2}+d \right) c e +b e \right) \textit{\_Z} , \mathit{index} =2\right)}{\RootOf \left(\textit{\_Z}^{2} c e +\RootOf \left(e \,\textit{\_Z}^{2}+d \right) b e +a e -c d +\left(2 \RootOf \left(e \,\textit{\_Z}^{2}+d \right) c e +b e \right) \textit{\_Z} , \mathit{index} =2\right)}\right) \ln \left(-\RootOf \left(e \,\textit{\_Z}^{2}+d \right)+x \right)+\ln \left(-\RootOf \left(e \,\textit{\_Z}^{2}+d \right)+x \right) \ln \left(c \,x^{2}+b x +a \right)-\dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+d \right)-x +\RootOf \left(\textit{\_Z}^{2} c e +\RootOf \left(e \,\textit{\_Z}^{2}+d \right) b e +a e -c d +\left(2 \RootOf \left(e \,\textit{\_Z}^{2}+d \right) c e +b e \right) \textit{\_Z} , \mathit{index} =1\right)}{\RootOf \left(\textit{\_Z}^{2} c e +\RootOf \left(e \,\textit{\_Z}^{2}+d \right) b e +a e -c d +\left(2 \RootOf \left(e \,\textit{\_Z}^{2}+d \right) c e +b e \right) \textit{\_Z} , \mathit{index} =1\right)}\right)-\dilog \left(\frac{\RootOf \left(e \,\textit{\_Z}^{2}+d \right)-x +\RootOf \left(\textit{\_Z}^{2} c e +\RootOf \left(e \,\textit{\_Z}^{2}+d \right) b e +a e -c d +\left(2 \RootOf \left(e \,\textit{\_Z}^{2}+d \right) c e +b e \right) \textit{\_Z} , \mathit{index} =2\right)}{\RootOf \left(\textit{\_Z}^{2} c e +\RootOf \left(e \,\textit{\_Z}^{2}+d \right) b e +a e -c d +\left(2 \RootOf \left(e \,\textit{\_Z}^{2}+d \right) c e +b e \right) \textit{\_Z} , \mathit{index} =2\right)}\right)\right)}{2 e \RootOf \left(e \,\textit{\_Z}^{2}+d \right)}+\frac{\left(-n \ln \left(c \,x^{2}+b x +a \right)+\ln \left(\left(c \,x^{2}+b x +a \right)^{n}\right)\right) \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}"," ",0,"(ln((c*x^2+b*x+a)^n)-n*ln(c*x^2+b*x+a))/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)+1/2*n/e*sum(1/_alpha*(ln(-_alpha+x)*ln(c*x^2+b*x+a)-ln(-_alpha+x)*ln((RootOf(_Z^2*c*e+(2*_alpha*c*e+b*e)*_Z+b*_alpha*e+a*e-c*d,index=1)-x+_alpha)/RootOf(_Z^2*c*e+(2*_alpha*c*e+b*e)*_Z+b*_alpha*e+a*e-c*d,index=1))-ln(-_alpha+x)*ln((RootOf(_Z^2*c*e+(2*_alpha*c*e+b*e)*_Z+b*_alpha*e+a*e-c*d,index=2)-x+_alpha)/RootOf(_Z^2*c*e+(2*_alpha*c*e+b*e)*_Z+b*_alpha*e+a*e-c*d,index=2))-dilog((RootOf(_Z^2*c*e+(2*_alpha*c*e+b*e)*_Z+b*_alpha*e+a*e-c*d,index=1)-x+_alpha)/RootOf(_Z^2*c*e+(2*_alpha*c*e+b*e)*_Z+b*_alpha*e+a*e-c*d,index=1))-dilog((RootOf(_Z^2*c*e+(2*_alpha*c*e+b*e)*_Z+b*_alpha*e+a*e-c*d,index=2)-x+_alpha)/RootOf(_Z^2*c*e+(2*_alpha*c*e+b*e)*_Z+b*_alpha*e+a*e-c*d,index=2))),_alpha=RootOf(_Z^2*e+d))+1/2*I/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*Pi*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*g*(c*x^2+b*x+a)^n)^2-1/2*I/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*Pi*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*g*(c*x^2+b*x+a)^n)*csgn(I*g)-1/2*I/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*Pi*csgn(I*g*(c*x^2+b*x+a)^n)^3+1/2*I/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*Pi*csgn(I*g*(c*x^2+b*x+a)^n)^2*csgn(I*g)+1/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*ln(g)","C"
95,1,764,702,1.170000," ","int(ln(g*(c*x^2+b*x+a)^n)/(f*x^2+e*x+d),x)","-\frac{i \pi  \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right) \mathrm{csgn}\left(i g \right) \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i g \left(c \,x^{2}+b x +a \right)^{n}\right)}{\sqrt{4 d f -e^{2}}}+\frac{i \pi  \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right) \mathrm{csgn}\left(i g \right) \mathrm{csgn}\left(i g \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}}{\sqrt{4 d f -e^{2}}}+\frac{i \pi  \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right) \mathrm{csgn}\left(i \left(c \,x^{2}+b x +a \right)^{n}\right) \mathrm{csgn}\left(i g \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}}{\sqrt{4 d f -e^{2}}}-\frac{i \pi  \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right) \mathrm{csgn}\left(i g \left(c \,x^{2}+b x +a \right)^{n}\right)^{3}}{\sqrt{4 d f -e^{2}}}+\frac{n \left(-\ln \left(\frac{\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right)-x +\RootOf \left(\textit{\_Z}^{2} c f +\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) b f -\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) c e +a f -c d +\left(2 \RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) c f +b f \right) \textit{\_Z} , \mathit{index} =1\right)}{\RootOf \left(\textit{\_Z}^{2} c f +\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) b f -\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) c e +a f -c d +\left(2 \RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) c f +b f \right) \textit{\_Z} , \mathit{index} =1\right)}\right) \ln \left(-\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right)+x \right)-\ln \left(\frac{\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right)-x +\RootOf \left(\textit{\_Z}^{2} c f +\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) b f -\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) c e +a f -c d +\left(2 \RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) c f +b f \right) \textit{\_Z} , \mathit{index} =2\right)}{\RootOf \left(\textit{\_Z}^{2} c f +\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) b f -\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) c e +a f -c d +\left(2 \RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) c f +b f \right) \textit{\_Z} , \mathit{index} =2\right)}\right) \ln \left(-\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right)+x \right)+\ln \left(-\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right)+x \right) \ln \left(c \,x^{2}+b x +a \right)-\dilog \left(\frac{\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right)-x +\RootOf \left(\textit{\_Z}^{2} c f +\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) b f -\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) c e +a f -c d +\left(2 \RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) c f +b f \right) \textit{\_Z} , \mathit{index} =1\right)}{\RootOf \left(\textit{\_Z}^{2} c f +\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) b f -\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) c e +a f -c d +\left(2 \RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) c f +b f \right) \textit{\_Z} , \mathit{index} =1\right)}\right)-\dilog \left(\frac{\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right)-x +\RootOf \left(\textit{\_Z}^{2} c f +\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) b f -\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) c e +a f -c d +\left(2 \RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) c f +b f \right) \textit{\_Z} , \mathit{index} =2\right)}{\RootOf \left(\textit{\_Z}^{2} c f +\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) b f -\RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) c e +a f -c d +\left(2 \RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) c f +b f \right) \textit{\_Z} , \mathit{index} =2\right)}\right)\right)}{2 \RootOf \left(f \,\textit{\_Z}^{2}+\textit{\_Z} e +d \right) f +e}+\frac{2 \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right) \ln \left(g \right)}{\sqrt{4 d f -e^{2}}}+\frac{2 \left(-n \ln \left(c \,x^{2}+b x +a \right)+\ln \left(\left(c \,x^{2}+b x +a \right)^{n}\right)\right) \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}}"," ",0,"2*(-n*ln(c*x^2+b*x+a)+ln((c*x^2+b*x+a)^n))/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))+n*sum((ln(-_alpha+x)*ln(c*x^2+b*x+a)-ln(-_alpha+x)*ln((RootOf(_Z^2*c*f+(2*_alpha*c*f+b*f)*_Z+b*_alpha*f-_alpha*c*e+a*f-c*d,index=1)-x+_alpha)/RootOf(_Z^2*c*f+(2*_alpha*c*f+b*f)*_Z+b*_alpha*f-_alpha*c*e+a*f-c*d,index=1))-ln(-_alpha+x)*ln((RootOf(_Z^2*c*f+(2*_alpha*c*f+b*f)*_Z+b*_alpha*f-_alpha*c*e+a*f-c*d,index=2)-x+_alpha)/RootOf(_Z^2*c*f+(2*_alpha*c*f+b*f)*_Z+b*_alpha*f-_alpha*c*e+a*f-c*d,index=2))-dilog((RootOf(_Z^2*c*f+(2*_alpha*c*f+b*f)*_Z+b*_alpha*f-_alpha*c*e+a*f-c*d,index=1)-x+_alpha)/RootOf(_Z^2*c*f+(2*_alpha*c*f+b*f)*_Z+b*_alpha*f-_alpha*c*e+a*f-c*d,index=1))-dilog((RootOf(_Z^2*c*f+(2*_alpha*c*f+b*f)*_Z+b*_alpha*f-_alpha*c*e+a*f-c*d,index=2)-x+_alpha)/RootOf(_Z^2*c*f+(2*_alpha*c*f+b*f)*_Z+b*_alpha*f-_alpha*c*e+a*f-c*d,index=2)))/(2*_alpha*f+e),_alpha=RootOf(_Z^2*f+_Z*e+d))+I/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*Pi*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*g*(c*x^2+b*x+a)^n)^2-I/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*Pi*csgn(I*(c*x^2+b*x+a)^n)*csgn(I*g*(c*x^2+b*x+a)^n)*csgn(I*g)-I/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*Pi*csgn(I*g*(c*x^2+b*x+a)^n)^3+I/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*Pi*csgn(I*g*(c*x^2+b*x+a)^n)^2*csgn(I*g)+2/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*ln(g)","C"
96,0,0,144,0.161000," ","int(ln(d*(c*x^2+b*x)^n)^2,x)","\int \ln \left(d \left(c \,x^{2}+b x \right)^{n}\right)^{2}\, dx"," ",0,"int(ln(d*(c*x^2+b*x)^n)^2,x)","F"
97,0,0,527,1.126000," ","int(ln(d*(c*x^2+b*x+a)^n)^2,x)","\int \ln \left(d \left(c \,x^{2}+b x +a \right)^{n}\right)^{2}\, dx"," ",0,"int(ln(d*(c*x^2+b*x+a)^n)^2,x)","F"
98,1,279,266,0.093000," ","int(x^2*ln(x^2+x+1)/(x^2+3*x+2),x)","x \ln \left(x^{2}+x +1\right)-\ln \left(\frac{-2 x -1+i \sqrt{3}}{1+i \sqrt{3}}\right) \ln \left(x +1\right)+4 \ln \left(\frac{-2 x -1+i \sqrt{3}}{3+i \sqrt{3}}\right) \ln \left(x +2\right)+4 \ln \left(\frac{2 x +1+i \sqrt{3}}{-3+i \sqrt{3}}\right) \ln \left(x +2\right)-\ln \left(\frac{2 x +1+i \sqrt{3}}{i \sqrt{3}-1}\right) \ln \left(x +1\right)+\ln \left(x +1\right) \ln \left(x^{2}+x +1\right)-4 \ln \left(x +2\right) \ln \left(x^{2}+x +1\right)-2 x -\dilog \left(\frac{-2 x -1+i \sqrt{3}}{1+i \sqrt{3}}\right)+4 \dilog \left(\frac{-2 x -1+i \sqrt{3}}{3+i \sqrt{3}}\right)+4 \dilog \left(\frac{2 x +1+i \sqrt{3}}{-3+i \sqrt{3}}\right)-\dilog \left(\frac{2 x +1+i \sqrt{3}}{i \sqrt{3}-1}\right)+\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)+\frac{\ln \left(x^{2}+x +1\right)}{2}"," ",0,"x*ln(x^2+x+1)-2*x+1/2*ln(x^2+x+1)+3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))-4*ln(x+2)*ln(x^2+x+1)+4*ln(x+2)*ln((-1-2*x+I*3^(1/2))/(3+I*3^(1/2)))+4*ln(x+2)*ln((1+2*x+I*3^(1/2))/(-3+I*3^(1/2)))+4*dilog((-1-2*x+I*3^(1/2))/(3+I*3^(1/2)))+4*dilog((1+2*x+I*3^(1/2))/(-3+I*3^(1/2)))+ln(x+1)*ln(x^2+x+1)-ln(x+1)*ln((-1-2*x+I*3^(1/2))/(1+I*3^(1/2)))-ln(x+1)*ln((1+2*x+I*3^(1/2))/(I*3^(1/2)-1))-dilog((-1-2*x+I*3^(1/2))/(1+I*3^(1/2)))-dilog((1+2*x+I*3^(1/2))/(I*3^(1/2)-1))","A"
99,0,0,288,0.096000," ","int(ln(x^2+x+1)^2,x)","\int \ln \left(x^{2}+x +1\right)^{2}\, dx"," ",0,"int(ln(x^2+x+1)^2,x)","F"
100,0,0,345,0.130000," ","int(ln(x^2+x-1)^2/x^3,x)","\int \frac{\ln \left(x^{2}+x -1\right)^{2}}{x^{3}}\, dx"," ",0,"int(ln(x^2+x-1)^2/x^3,x)","F"
101,0,0,132,0.073000," ","int(x^3*ln(-1+4*x+4*((x-1)*x)^(1/2)),x)","\int x^{3} \ln \left(4 x -1+4 \sqrt{\left(x -1\right) x}\right)\, dx"," ",0,"int(x^3*ln(-1+4*x+4*((x-1)*x)^(1/2)),x)","F"
102,0,0,115,0.072000," ","int(x^2*ln(4*x-1+4*((x-1)*x)^(1/2)),x)","\int x^{2} \ln \left(4 x -1+4 \sqrt{\left(x -1\right) x}\right)\, dx"," ",0,"int(x^2*ln(4*x-1+4*((x-1)*x)^(1/2)),x)","F"
103,0,0,99,0.079000," ","int(x*ln(4*x-1+4*((x-1)*x)^(1/2)),x)","\int x \ln \left(4 x -1+4 \sqrt{\left(x -1\right) x}\right)\, dx"," ",0,"int(x*ln(4*x-1+4*((x-1)*x)^(1/2)),x)","F"
104,1,80,75,0.104000," ","int(ln(4*x-1+4*((x-1)*x)^(1/2)),x)","x \ln \left(4 x -1+4 \sqrt{\left(x -1\right) x}\right)-\frac{x}{2}-\frac{\arctanh \left(\frac{-\frac{40 x}{3}+\frac{4}{3}}{\sqrt{-80 x +64 \left(x +\frac{1}{8}\right)^{2}-1}}\right)}{16}+\frac{\ln \left(8 x +1\right)}{16}-\frac{7 \ln \left(x -\frac{1}{2}+\sqrt{x^{2}-x}\right)}{16}-\frac{\sqrt{x^{2}-x}}{2}"," ",0,"x*ln(4*x-1+4*((x-1)*x)^(1/2))-7/16*ln(x-1/2+(x^2-x)^(1/2))-1/16*arctanh(32/3*(1/8-5/4*x)/(64*(x+1/8)^2-80*x-1)^(1/2))-1/2*(x^2-x)^(1/2)-1/2*x+1/16*ln(1+8*x)","A"
105,0,0,23,0.083000," ","int(ln(4*x-1+4*((x-1)*x)^(1/2))/x,x)","\int \frac{\ln \left(4 x -1+4 \sqrt{\left(x -1\right) x}\right)}{x}\, dx"," ",0,"int(ln(4*x-1+4*((x-1)*x)^(1/2))/x,x)","F"
106,0,0,68,0.072000," ","int(ln(4*x-1+4*((x-1)*x)^(1/2))/x^2,x)","\int \frac{\ln \left(4 x -1+4 \sqrt{\left(x -1\right) x}\right)}{x^{2}}\, dx"," ",0,"int(ln(4*x-1+4*((x-1)*x)^(1/2))/x^2,x)","F"
107,0,0,87,0.076000," ","int(ln(4*x-1+4*((x-1)*x)^(1/2))/x^3,x)","\int \frac{\ln \left(4 x -1+4 \sqrt{\left(x -1\right) x}\right)}{x^{3}}\, dx"," ",0,"int(ln(4*x-1+4*((x-1)*x)^(1/2))/x^3,x)","F"
108,0,0,127,0.075000," ","int(x^(3/2)*ln(4*x-1+4*((x-1)*x)^(1/2)),x)","\int x^{\frac{3}{2}} \ln \left(4 x -1+4 \sqrt{\left(x -1\right) x}\right)\, dx"," ",0,"int(x^(3/2)*ln(4*x-1+4*((x-1)*x)^(1/2)),x)","F"
109,0,0,108,0.072000," ","int(x^(1/2)*ln(4*x-1+4*((x-1)*x)^(1/2)),x)","\int \sqrt{x}\, \ln \left(4 x -1+4 \sqrt{\left(x -1\right) x}\right)\, dx"," ",0,"int(x^(1/2)*ln(4*x-1+4*((x-1)*x)^(1/2)),x)","F"
110,0,0,89,0.076000," ","int(ln(4*x-1+4*((x-1)*x)^(1/2))/x^(1/2),x)","\int \frac{\ln \left(4 x -1+4 \sqrt{\left(x -1\right) x}\right)}{\sqrt{x}}\, dx"," ",0,"int(ln(4*x-1+4*((x-1)*x)^(1/2))/x^(1/2),x)","F"
111,0,0,86,0.076000," ","int(ln(4*x-1+4*((x-1)*x)^(1/2))/x^(3/2),x)","\int \frac{\ln \left(4 x -1+4 \sqrt{\left(x -1\right) x}\right)}{x^{\frac{3}{2}}}\, dx"," ",0,"int(ln(4*x-1+4*((x-1)*x)^(1/2))/x^(3/2),x)","F"
112,0,0,105,0.076000," ","int(ln(4*x-1+4*((x-1)*x)^(1/2))/x^(5/2),x)","\int \frac{\ln \left(4 x -1+4 \sqrt{\left(x -1\right) x}\right)}{x^{\frac{5}{2}}}\, dx"," ",0,"int(ln(4*x-1+4*((x-1)*x)^(1/2))/x^(5/2),x)","F"
113,1,84,83,0.079000," ","int(x^3*ln(b*exp(x)+a),x)","-\frac{x^{4} \ln \left(\frac{b \,{\mathrm e}^{x}}{a}+1\right)}{4}+\frac{x^{4} \ln \left(b \,{\mathrm e}^{x}+a \right)}{4}-x^{3} \polylog \left(2, -\frac{b \,{\mathrm e}^{x}}{a}\right)+3 x^{2} \polylog \left(3, -\frac{b \,{\mathrm e}^{x}}{a}\right)-6 x \polylog \left(4, -\frac{b \,{\mathrm e}^{x}}{a}\right)+6 \polylog \left(5, -\frac{b \,{\mathrm e}^{x}}{a}\right)"," ",0,"1/4*x^4*ln(b*exp(x)+a)-1/4*x^4*ln(1+b*exp(x)/a)-x^3*polylog(2,-b*exp(x)/a)+3*x^2*polylog(3,-b*exp(x)/a)-6*x*polylog(4,-b*exp(x)/a)+6*polylog(5,-b*exp(x)/a)","A"
114,1,69,68,0.071000," ","int(x^2*ln(b*exp(x)+a),x)","-\frac{x^{3} \ln \left(\frac{b \,{\mathrm e}^{x}}{a}+1\right)}{3}+\frac{x^{3} \ln \left(b \,{\mathrm e}^{x}+a \right)}{3}-x^{2} \polylog \left(2, -\frac{b \,{\mathrm e}^{x}}{a}\right)+2 x \polylog \left(3, -\frac{b \,{\mathrm e}^{x}}{a}\right)-2 \polylog \left(4, -\frac{b \,{\mathrm e}^{x}}{a}\right)"," ",0,"1/3*x^3*ln(b*exp(x)+a)-1/3*x^3*ln(1/a*b*exp(x)+1)-x^2*polylog(2,-1/a*b*exp(x))+2*x*polylog(3,-1/a*b*exp(x))-2*polylog(4,-1/a*b*exp(x))","A"
115,1,52,51,0.078000," ","int(x*ln(b*exp(x)+a),x)","-\frac{x^{2} \ln \left(\frac{b \,{\mathrm e}^{x}}{a}+1\right)}{2}+\frac{x^{2} \ln \left(b \,{\mathrm e}^{x}+a \right)}{2}-x \polylog \left(2, -\frac{b \,{\mathrm e}^{x}}{a}\right)+\polylog \left(3, -\frac{b \,{\mathrm e}^{x}}{a}\right)"," ",0,"1/2*x^2*ln(b*exp(x)+a)-1/2*x^2*ln(1/a*b*exp(x)+1)-x*polylog(2,-1/a*b*exp(x))+polylog(3,-1/a*b*exp(x))","A"
116,1,28,35,0.077000," ","int(ln(b*exp(x)+a),x)","\ln \left(-\frac{b \,{\mathrm e}^{x}}{a}\right) \ln \left(b \,{\mathrm e}^{x}+a \right)+\dilog \left(-\frac{b \,{\mathrm e}^{x}}{a}\right)"," ",0,"dilog(-1/a*b*exp(x))+ln(b*exp(x)+a)*ln(-1/a*b*exp(x))","A"
117,0,0,13,0.103000," ","int(ln(b*exp(x)+a)/x,x)","\int \frac{\ln \left(b \,{\mathrm e}^{x}+a \right)}{x}\, dx"," ",0,"int(ln(b*exp(x)+a)/x,x)","F"
118,1,601,132,0.426000," ","int(x^3*ln(1+e*(f^((b*x+a)*c))^n),x)","\frac{x^{4} \ln \left(e \left(f^{\left(b x +a \right) c}\right)^{n}+1\right)}{4}-\frac{x^{4} \ln \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+1\right)}{4}-\frac{x^{3} \dilog \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+1\right)}{b c n \ln \left(f \right)}+\frac{3 x^{2} \dilog \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+1\right) \ln \left(f^{\left(b x +a \right) c}\right)}{b^{2} c^{2} n \ln \left(f \right)^{2}}-\frac{3 x^{2} \polylog \left(2, -e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}\right) \ln \left(f^{\left(b x +a \right) c}\right)}{b^{2} c^{2} n \ln \left(f \right)^{2}}+\frac{3 x^{2} \polylog \left(3, -e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}\right)}{b^{2} c^{2} n^{2} \ln \left(f \right)^{2}}-\frac{3 x \dilog \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+1\right) \ln \left(f^{\left(b x +a \right) c}\right)^{2}}{b^{3} c^{3} n \ln \left(f \right)^{3}}+\frac{3 x \polylog \left(2, -e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}\right) \ln \left(f^{\left(b x +a \right) c}\right)^{2}}{b^{3} c^{3} n \ln \left(f \right)^{3}}+\frac{\dilog \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+1\right) \ln \left(f^{\left(b x +a \right) c}\right)^{3}}{b^{4} c^{4} n \ln \left(f \right)^{4}}-\frac{\polylog \left(2, -e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}\right) \ln \left(f^{\left(b x +a \right) c}\right)^{3}}{b^{4} c^{4} n \ln \left(f \right)^{4}}-\frac{6 x \polylog \left(4, -e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}\right)}{b^{3} c^{3} n^{3} \ln \left(f \right)^{3}}+\frac{6 \polylog \left(5, -e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}\right)}{b^{4} c^{4} n^{4} \ln \left(f \right)^{4}}"," ",0,"1/4*x^4*ln(1+e*(f^((b*x+a)*c))^n)+6/c^4/ln(f)^4/b^4/n^4*polylog(5,-e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)+3/c^2/ln(f)^2/b^2/n*dilog(1+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*ln(f^((b*x+a)*c))*x^2-3/c^3/ln(f)^3/b^3/n*dilog(1+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*ln(f^((b*x+a)*c))^2*x+3/c^3/ln(f)^3/b^3/n*polylog(2,-e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*ln(f^((b*x+a)*c))^2*x-3/c^2/ln(f)^2/b^2/n*polylog(2,-e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*ln(f^((b*x+a)*c))*x^2-1/4*ln(1+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*x^4-6/c^3/ln(f)^3/b^3/n^3*polylog(4,-e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*x+3/c^2/ln(f)^2/b^2/n^2*polylog(3,-e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*x^2-1/c^4/ln(f)^4/b^4/n*polylog(2,-e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*ln(f^((b*x+a)*c))^3-1/c/ln(f)/b/n*dilog(1+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*x^3+1/c^4/ln(f)^4/b^4/n*dilog(1+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*ln(f^((b*x+a)*c))^3","B"
119,1,430,98,0.349000," ","int(x^2*ln(e*(f^((b*x+a)*c))^n+1),x)","\frac{x^{3} \ln \left(e \left(f^{\left(b x +a \right) c}\right)^{n}+1\right)}{3}-\frac{x^{3} \ln \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+1\right)}{3}-\frac{x^{2} \dilog \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+1\right)}{b c n \ln \left(f \right)}+\frac{2 x \dilog \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+1\right) \ln \left(f^{\left(b x +a \right) c}\right)}{b^{2} c^{2} n \ln \left(f \right)^{2}}-\frac{2 x \polylog \left(2, -e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}\right) \ln \left(f^{\left(b x +a \right) c}\right)}{b^{2} c^{2} n \ln \left(f \right)^{2}}+\frac{2 x \polylog \left(3, -e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}\right)}{b^{2} c^{2} n^{2} \ln \left(f \right)^{2}}-\frac{\dilog \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+1\right) \ln \left(f^{\left(b x +a \right) c}\right)^{2}}{b^{3} c^{3} n \ln \left(f \right)^{3}}+\frac{\polylog \left(2, -e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}\right) \ln \left(f^{\left(b x +a \right) c}\right)^{2}}{b^{3} c^{3} n \ln \left(f \right)^{3}}-\frac{2 \polylog \left(4, -e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}\right)}{b^{3} c^{3} n^{3} \ln \left(f \right)^{3}}"," ",0,"1/3*x^3*ln(e*(f^((b*x+a)*c))^n+1)-2/c^3/ln(f)^3/b^3/n^3*polylog(4,-e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)-1/c/ln(f)/b/n*dilog(e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+1)*x^2+2/c^2/ln(f)^2/b^2/n*dilog(e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+1)*ln(f^((b*x+a)*c))*x-1/c^3/ln(f)^3/b^3/n*dilog(e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+1)*ln(f^((b*x+a)*c))^2-2/c^2/ln(f)^2/b^2/n*polylog(2,-e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*ln(f^((b*x+a)*c))*x+1/c^3/ln(f)^3/b^3/n*polylog(2,-e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*ln(f^((b*x+a)*c))^2+2/c^2/ln(f)^2/b^2/n^2*polylog(3,-e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*x-1/3*ln(e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+1)*x^3","B"
120,1,262,63,0.346000," ","int(x*ln(e*(f^((b*x+a)*c))^n+1),x)","\frac{x^{2} \ln \left(e \left(f^{\left(b x +a \right) c}\right)^{n}+1\right)}{2}-\frac{x^{2} \ln \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+1\right)}{2}-\frac{x \dilog \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+1\right)}{b c n \ln \left(f \right)}+\frac{\dilog \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+1\right) \ln \left(f^{\left(b x +a \right) c}\right)}{b^{2} c^{2} n \ln \left(f \right)^{2}}-\frac{\polylog \left(2, -e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}\right) \ln \left(f^{\left(b x +a \right) c}\right)}{b^{2} c^{2} n \ln \left(f \right)^{2}}+\frac{\polylog \left(3, -e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}\right)}{b^{2} c^{2} n^{2} \ln \left(f \right)^{2}}"," ",0,"1/2*x^2*ln(e*(f^((b*x+a)*c))^n+1)-1/2*ln(e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+1)*x^2-1/c^2/ln(f)^2/b^2/n*polylog(2,-e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*ln(f^((b*x+a)*c))+1/c^2/ln(f)^2/b^2/n^2*polylog(3,-e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)-1/c/ln(f)/b/n*dilog(e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+1)*x+1/c^2/ln(f)^2/b^2/n*dilog(e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+1)*ln(f^((b*x+a)*c))","B"
121,1,32,31,0.072000," ","int(ln(e*(f^((b*x+a)*c))^n+1),x)","-\frac{\dilog \left(e \left(f^{\left(b x +a \right) c}\right)^{n}+1\right)}{b c n \ln \left(f \right)}"," ",0,"-1/b/c/ln(f)/n*dilog(e*(f^((b*x+a)*c))^n+1)","A"
122,0,0,22,0.245000," ","int(ln(e*(f^((b*x+a)*c))^n+1)/x,x)","\int \frac{\ln \left(e \left(f^{\left(b x +a \right) c}\right)^{n}+1\right)}{x}\, dx"," ",0,"int(ln(e*(f^((b*x+a)*c))^n+1)/x,x)","F"
123,1,1276,189,0.363000," ","int(x^3*ln(d+e*(f^((b*x+a)*c))^n),x)","\frac{x^{4} \ln \left(e \left(f^{\left(b x +a \right) c}\right)^{n}+d \right)}{4}-\frac{x^{4} \ln \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d \right)}{4}-\frac{x^{3} \ln \left(f^{\left(b x +a \right) c}\right) \ln \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d}{d}\right)}{b c \ln \left(f \right)}+\frac{x^{3} \ln \left(f^{\left(b x +a \right) c}\right) \ln \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d \right)}{b c \ln \left(f \right)}-\frac{x^{3} \dilog \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d}{d}\right)}{b c n \ln \left(f \right)}+\frac{3 x^{2} \ln \left(f^{\left(b x +a \right) c}\right)^{2} \ln \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d}{d}\right)}{b^{2} c^{2} \ln \left(f \right)^{2}}-\frac{3 x^{2} \ln \left(f^{\left(b x +a \right) c}\right)^{2} \ln \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}}{d}+1\right)}{2 b^{2} c^{2} \ln \left(f \right)^{2}}-\frac{3 x^{2} \ln \left(f^{\left(b x +a \right) c}\right)^{2} \ln \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d \right)}{2 b^{2} c^{2} \ln \left(f \right)^{2}}+\frac{3 x^{2} \dilog \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d}{d}\right) \ln \left(f^{\left(b x +a \right) c}\right)}{b^{2} c^{2} n \ln \left(f \right)^{2}}-\frac{3 x^{2} \polylog \left(2, -\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}}{d}\right) \ln \left(f^{\left(b x +a \right) c}\right)}{b^{2} c^{2} n \ln \left(f \right)^{2}}-\frac{3 x \ln \left(f^{\left(b x +a \right) c}\right)^{3} \ln \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d}{d}\right)}{b^{3} c^{3} \ln \left(f \right)^{3}}+\frac{2 x \ln \left(f^{\left(b x +a \right) c}\right)^{3} \ln \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}}{d}+1\right)}{b^{3} c^{3} \ln \left(f \right)^{3}}+\frac{x \ln \left(f^{\left(b x +a \right) c}\right)^{3} \ln \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d \right)}{b^{3} c^{3} \ln \left(f \right)^{3}}+\frac{3 x^{2} \polylog \left(3, -\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}}{d}\right)}{b^{2} c^{2} n^{2} \ln \left(f \right)^{2}}-\frac{3 x \dilog \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d}{d}\right) \ln \left(f^{\left(b x +a \right) c}\right)^{2}}{b^{3} c^{3} n \ln \left(f \right)^{3}}+\frac{3 x \polylog \left(2, -\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}}{d}\right) \ln \left(f^{\left(b x +a \right) c}\right)^{2}}{b^{3} c^{3} n \ln \left(f \right)^{3}}+\frac{\ln \left(f^{\left(b x +a \right) c}\right)^{4} \ln \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d}{d}\right)}{b^{4} c^{4} \ln \left(f \right)^{4}}-\frac{3 \ln \left(f^{\left(b x +a \right) c}\right)^{4} \ln \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}}{d}+1\right)}{4 b^{4} c^{4} \ln \left(f \right)^{4}}-\frac{\ln \left(f^{\left(b x +a \right) c}\right)^{4} \ln \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d \right)}{4 b^{4} c^{4} \ln \left(f \right)^{4}}+\frac{\dilog \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d}{d}\right) \ln \left(f^{\left(b x +a \right) c}\right)^{3}}{b^{4} c^{4} n \ln \left(f \right)^{4}}-\frac{\polylog \left(2, -\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}}{d}\right) \ln \left(f^{\left(b x +a \right) c}\right)^{3}}{b^{4} c^{4} n \ln \left(f \right)^{4}}-\frac{6 x \polylog \left(4, -\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}}{d}\right)}{b^{3} c^{3} n^{3} \ln \left(f \right)^{3}}+\frac{6 \polylog \left(5, -\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}}{d}\right)}{b^{4} c^{4} n^{4} \ln \left(f \right)^{4}}"," ",0,"1/4*x^4*ln(d+e*(f^((b*x+a)*c))^n)-1/c^4/ln(f)^4/b^4/n*polylog(2,-e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n/d)*ln(f^((b*x+a)*c))^3-3/4/c^4/ln(f)^4/b^4*ln(1+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n/d)*ln(f^((b*x+a)*c))^4-6/c^3/ln(f)^3/b^3/n^3*polylog(4,-e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n/d)*x+1/c^4/ln(f)^4/b^4*ln((d+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)/d)*ln(f^((b*x+a)*c))^4-1/c/ln(f)/b/n*dilog((d+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)/d)*x^3-3/c^3/ln(f)^3/b^3/n*dilog((d+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)/d)*ln(f^((b*x+a)*c))^2*x+6/c^4/ln(f)^4/b^4/n^4*polylog(5,-e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n/d)-3/c^2/ln(f)^2/b^2/n*polylog(2,-e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n/d)*ln(f^((b*x+a)*c))*x^2-1/4*ln(d+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*x^4-3/2/c^2/ln(f)^2/b^2*ln(1+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n/d)*x^2*ln(f^((b*x+a)*c))^2+2/c^3/ln(f)^3/b^3*ln(1+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n/d)*x*ln(f^((b*x+a)*c))^3-1/c/ln(f)/b*ln((d+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)/d)*x^3*ln(f^((b*x+a)*c))+3/c^2/ln(f)^2/b^2*ln((d+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)/d)*x^2*ln(f^((b*x+a)*c))^2-3/c^3/ln(f)^3/b^3*ln((d+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)/d)*x*ln(f^((b*x+a)*c))^3+1/c/ln(f)/b*ln(d+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*ln(f^((b*x+a)*c))*x^3-3/2/c^2/ln(f)^2/b^2*ln(d+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*ln(f^((b*x+a)*c))^2*x^2+1/c^3/ln(f)^3/b^3*ln(d+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*ln(f^((b*x+a)*c))^3*x+3/c^2/ln(f)^2/b^2/n*dilog((d+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)/d)*ln(f^((b*x+a)*c))*x^2+1/c^4/ln(f)^4/b^4/n*dilog((d+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)/d)*ln(f^((b*x+a)*c))^3+3/c^2/ln(f)^2/b^2/n^2*polylog(3,-e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n/d)*x^2-1/4/c^4/ln(f)^4/b^4*ln(d+e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*ln(f^((b*x+a)*c))^4+3/c^3/ln(f)^3/b^3/n*polylog(2,-e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n/d)*ln(f^((b*x+a)*c))^2*x","B"
124,1,916,152,0.352000," ","int(x^2*ln(e*(f^((b*x+a)*c))^n+d),x)","\frac{x^{3} \ln \left(e \left(f^{\left(b x +a \right) c}\right)^{n}+d \right)}{3}-\frac{x^{3} \ln \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d \right)}{3}-\frac{x^{2} \ln \left(f^{\left(b x +a \right) c}\right) \ln \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d}{d}\right)}{b c \ln \left(f \right)}+\frac{x^{2} \ln \left(f^{\left(b x +a \right) c}\right) \ln \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d \right)}{b c \ln \left(f \right)}-\frac{x^{2} \dilog \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d}{d}\right)}{b c n \ln \left(f \right)}+\frac{2 x \ln \left(f^{\left(b x +a \right) c}\right)^{2} \ln \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d}{d}\right)}{b^{2} c^{2} \ln \left(f \right)^{2}}-\frac{x \ln \left(f^{\left(b x +a \right) c}\right)^{2} \ln \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}}{d}+1\right)}{b^{2} c^{2} \ln \left(f \right)^{2}}-\frac{x \ln \left(f^{\left(b x +a \right) c}\right)^{2} \ln \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d \right)}{b^{2} c^{2} \ln \left(f \right)^{2}}+\frac{2 x \dilog \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d}{d}\right) \ln \left(f^{\left(b x +a \right) c}\right)}{b^{2} c^{2} n \ln \left(f \right)^{2}}-\frac{2 x \polylog \left(2, -\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}}{d}\right) \ln \left(f^{\left(b x +a \right) c}\right)}{b^{2} c^{2} n \ln \left(f \right)^{2}}-\frac{\ln \left(f^{\left(b x +a \right) c}\right)^{3} \ln \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d}{d}\right)}{b^{3} c^{3} \ln \left(f \right)^{3}}+\frac{2 \ln \left(f^{\left(b x +a \right) c}\right)^{3} \ln \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}}{d}+1\right)}{3 b^{3} c^{3} \ln \left(f \right)^{3}}+\frac{\ln \left(f^{\left(b x +a \right) c}\right)^{3} \ln \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d \right)}{3 b^{3} c^{3} \ln \left(f \right)^{3}}+\frac{2 x \polylog \left(3, -\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}}{d}\right)}{b^{2} c^{2} n^{2} \ln \left(f \right)^{2}}-\frac{\dilog \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d}{d}\right) \ln \left(f^{\left(b x +a \right) c}\right)^{2}}{b^{3} c^{3} n \ln \left(f \right)^{3}}+\frac{\polylog \left(2, -\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}}{d}\right) \ln \left(f^{\left(b x +a \right) c}\right)^{2}}{b^{3} c^{3} n \ln \left(f \right)^{3}}-\frac{2 \polylog \left(4, -\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}}{d}\right)}{b^{3} c^{3} n^{3} \ln \left(f \right)^{3}}"," ",0,"1/3*x^3*ln(e*(f^((b*x+a)*c))^n+d)-2/c^2/ln(f)^2/b^2/n*polylog(2,-1/d*e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*ln(f^((b*x+a)*c))*x-1/c^2/ln(f)^2/b^2*ln(1/d*e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+1)*x*ln(f^((b*x+a)*c))^2-1/c/ln(f)/b*ln((e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+d)/d)*x^2*ln(f^((b*x+a)*c))+2/c^2/ln(f)^2/b^2*ln((e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+d)/d)*x*ln(f^((b*x+a)*c))^2+2/c^2/ln(f)^2/b^2/n*dilog((e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+d)/d)*ln(f^((b*x+a)*c))*x+1/c/ln(f)/b*ln(e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+d)*ln(f^((b*x+a)*c))*x^2-1/c/ln(f)/b/n*dilog((e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+d)/d)*x^2-1/c^2/ln(f)^2/b^2*ln(e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+d)*ln(f^((b*x+a)*c))^2*x-2/c^3/ln(f)^3/b^3/n^3*polylog(4,-1/d*e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)-1/c^3/ln(f)^3/b^3/n*dilog((e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+d)/d)*ln(f^((b*x+a)*c))^2+1/c^3/ln(f)^3/b^3/n*polylog(2,-1/d*e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*ln(f^((b*x+a)*c))^2-1/3*ln(e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+d)*x^3+1/3/c^3/ln(f)^3/b^3*ln(e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+d)*ln(f^((b*x+a)*c))^3-1/c^3/ln(f)^3/b^3*ln((e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+d)/d)*ln(f^((b*x+a)*c))^3+2/3/c^3/ln(f)^3/b^3*ln(1/d*e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+1)*ln(f^((b*x+a)*c))^3+2/c^2/ln(f)^2/b^2/n^2*polylog(3,-1/d*e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*x","B"
125,1,558,114,0.344000," ","int(x*ln(e*(f^((b*x+a)*c))^n+d),x)","\frac{x^{2} \ln \left(e \left(f^{\left(b x +a \right) c}\right)^{n}+d \right)}{2}-\frac{x^{2} \ln \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d \right)}{2}-\frac{x \ln \left(f^{\left(b x +a \right) c}\right) \ln \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d}{d}\right)}{b c \ln \left(f \right)}+\frac{x \ln \left(f^{\left(b x +a \right) c}\right) \ln \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d \right)}{b c \ln \left(f \right)}-\frac{x \dilog \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d}{d}\right)}{b c n \ln \left(f \right)}+\frac{\ln \left(f^{\left(b x +a \right) c}\right)^{2} \ln \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d}{d}\right)}{b^{2} c^{2} \ln \left(f \right)^{2}}-\frac{\ln \left(f^{\left(b x +a \right) c}\right)^{2} \ln \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}}{d}+1\right)}{2 b^{2} c^{2} \ln \left(f \right)^{2}}-\frac{\ln \left(f^{\left(b x +a \right) c}\right)^{2} \ln \left(e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d \right)}{2 b^{2} c^{2} \ln \left(f \right)^{2}}+\frac{\dilog \left(\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}+d}{d}\right) \ln \left(f^{\left(b x +a \right) c}\right)}{b^{2} c^{2} n \ln \left(f \right)^{2}}-\frac{\polylog \left(2, -\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}}{d}\right) \ln \left(f^{\left(b x +a \right) c}\right)}{b^{2} c^{2} n \ln \left(f \right)^{2}}+\frac{\polylog \left(3, -\frac{e \,f^{b c n x} f^{-b c n x} \left(f^{\left(b x +a \right) c}\right)^{n}}{d}\right)}{b^{2} c^{2} n^{2} \ln \left(f \right)^{2}}"," ",0,"1/2*x^2*ln(e*(f^((b*x+a)*c))^n+d)+1/c/ln(f)/b*ln(e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+d)*ln(f^((b*x+a)*c))*x-1/c/ln(f)/b*ln((e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+d)/d)*x*ln(f^((b*x+a)*c))+1/c^2/ln(f)^2/b^2/n^2*polylog(3,-1/d*e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)-1/2*ln(e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+d)*x^2-1/2/c^2/ln(f)^2/b^2*ln(e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+d)*ln(f^((b*x+a)*c))^2-1/c/ln(f)/b/n*dilog((e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+d)/d)*x+1/c^2/ln(f)^2/b^2/n*dilog((e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+d)/d)*ln(f^((b*x+a)*c))+1/c^2/ln(f)^2/b^2*ln((e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+d)/d)*ln(f^((b*x+a)*c))^2-1/2/c^2/ln(f)^2/b^2*ln(1/d*e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n+1)*ln(f^((b*x+a)*c))^2-1/c^2/ln(f)^2/b^2/n*polylog(2,-1/d*e*f^(b*c*n*x)*f^(-b*c*n*x)*(f^((b*x+a)*c))^n)*ln(f^((b*x+a)*c))","B"
126,1,82,75,0.080000," ","int(ln(e*(f^((b*x+a)*c))^n+d),x)","\frac{\ln \left(-\frac{e \left(f^{\left(b x +a \right) c}\right)^{n}}{d}\right) \ln \left(e \left(f^{\left(b x +a \right) c}\right)^{n}+d \right)}{b c n \ln \left(f \right)}+\frac{\dilog \left(-\frac{e \left(f^{\left(b x +a \right) c}\right)^{n}}{d}\right)}{b c n \ln \left(f \right)}"," ",0,"1/b/c/ln(f)/n*ln(e*(f^((b*x+a)*c))^n+d)*ln(-e*(f^((b*x+a)*c))^n/d)+1/b/c/ln(f)/n*dilog(-e*(f^((b*x+a)*c))^n/d)","A"
127,0,0,22,0.240000," ","int(ln(e*(f^((b*x+a)*c))^n+d)/x,x)","\int \frac{\ln \left(e \left(f^{\left(b x +a \right) c}\right)^{n}+d \right)}{x}\, dx"," ",0,"int(ln(e*(f^((b*x+a)*c))^n+d)/x,x)","F"
128,1,138,39,0.153000," ","int(ln(b*(F^((d*x+c)*e))^n+Pi),x)","-\frac{\ln \left(\frac{b \left(F^{\left(d x +c \right) e}\right)^{n}+\pi}{\pi}\right) \ln \left(-\frac{b \left(F^{\left(d x +c \right) e}\right)^{n}}{\pi}\right)}{d e n \ln \left(F \right)}+\frac{\ln \left(-\frac{b \left(F^{\left(d x +c \right) e}\right)^{n}}{\pi}\right) \ln \left(b \left(F^{\left(d x +c \right) e}\right)^{n}+\pi \right)}{d e n \ln \left(F \right)}-\frac{\dilog \left(\frac{b \left(F^{\left(d x +c \right) e}\right)^{n}+\pi}{\pi}\right)}{d e n \ln \left(F \right)}"," ",0,"-1/d/e/ln(F)/n*ln(-b*(F^((d*x+c)*e))^n/Pi)*ln((b*(F^((d*x+c)*e))^n+Pi)/Pi)+1/d/e/ln(F)/n*ln(-b*(F^((d*x+c)*e))^n/Pi)*ln(b*(F^((d*x+c)*e))^n+Pi)-1/d/e/ln(F)/n*dilog((b*(F^((d*x+c)*e))^n+Pi)/Pi)","B"
129,1,6,5,0.059000," ","int(1/x/(3+ln(x)),x)","\ln \left(\ln \left(x \right)+3\right)"," ",0,"ln(3+ln(x))","A"
130,1,9,8,0.066000," ","int((1+ln(x))^(1/2)/x,x)","\frac{2 \left(\ln \left(x \right)+1\right)^{\frac{3}{2}}}{3}"," ",0,"2/3*(1+ln(x))^(3/2)","A"
131,1,33,8,0.060000," ","int((ln(x)+1)^5/x,x)","\frac{\ln \left(x \right)^{6}}{6}+\ln \left(x \right)^{5}+\frac{5 \ln \left(x \right)^{4}}{2}+\frac{10 \ln \left(x \right)^{3}}{3}+\frac{5 \ln \left(x \right)^{2}}{2}+\ln \left(x \right)+\frac{1}{6}"," ",0,"1/6*ln(x)^6+ln(x)^5+5/2*ln(x)^4+10/3*ln(x)^3+5/2*ln(x)^2+ln(x)+1/6","B"
132,1,7,6,0.060000," ","int(1/x/ln(x)^(1/2),x)","2 \sqrt{\ln \left(x \right)}"," ",0,"2*ln(x)^(1/2)","A"
133,1,4,3,0.061000," ","int(1/x/(1+ln(x)^2),x)","\arctan \left(\ln \left(x \right)\right)"," ",0,"arctan(ln(x))","A"
134,1,13,12,0.067000," ","int(1/x/(-3+ln(x)^2)^(1/2),x)","\ln \left(\ln \left(x \right)+\sqrt{\ln \left(x \right)^{2}-3}\right)"," ",0,"ln(ln(x)+(-3+ln(x)^2)^(1/2))","A"
135,1,8,7,0.070000," ","int(1/x/(4-9*ln(x)^2)^(1/2),x)","\frac{\arcsin \left(\frac{3 \ln \left(x \right)}{2}\right)}{3}"," ",0,"1/3*arcsin(3/2*ln(x))","A"
136,1,6,5,0.066000," ","int(1/x/(4+ln(x)^2)^(1/2),x)","\arcsinh \left(\frac{\ln \left(x \right)}{2}\right)"," ",0,"arcsinh(1/2*ln(x))","A"
137,1,87,81,0.066000," ","int(1/x/(2+3*ln(6*x)^3),x)","\frac{2^{\frac{1}{3}} 3^{\frac{1}{6}} \arctan \left(\frac{\sqrt{3}\, \left(2^{\frac{2}{3}} 3^{\frac{1}{3}} \ln \left(6 x \right)-1\right)}{3}\right)}{6}+\frac{2^{\frac{1}{3}} 3^{\frac{2}{3}} \ln \left(\ln \left(6 x \right)+\frac{2^{\frac{1}{3}} 3^{\frac{2}{3}}}{3}\right)}{18}-\frac{2^{\frac{1}{3}} 3^{\frac{2}{3}} \ln \left(\ln \left(6 x \right)^{2}-\frac{2^{\frac{1}{3}} 3^{\frac{2}{3}} \ln \left(6 x \right)}{3}+\frac{2^{\frac{2}{3}} 3^{\frac{1}{3}}}{3}\right)}{36}"," ",0,"1/18*2^(1/3)*3^(2/3)*ln(ln(6*x)+1/3*2^(1/3)*3^(2/3))-1/36*2^(1/3)*3^(2/3)*ln(ln(6*x)^2-1/3*2^(1/3)*3^(2/3)*ln(6*x)+1/3*2^(2/3)*3^(1/3))+1/6*2^(1/3)*3^(1/6)*arctan(1/3*3^(1/2)*(2^(2/3)*3^(1/3)*ln(6*x)-1))","A"
138,1,10,9,0.063000," ","int(ln(ln(6*x))/x/ln(6*x),x)","\frac{\ln \left(\ln \left(6 x \right)\right)^{2}}{2}"," ",0,"1/2*ln(ln(6*x))^2","A"
139,1,10,9,0.073000," ","int(2^ln(x)/x,x)","\frac{2^{\ln \left(x \right)}}{\ln \left(2\right)}"," ",0,"2^ln(x)/ln(2)","A"
140,1,14,13,0.307000," ","int(sin(ln(x))^2/x,x)","-\frac{\cos \left(\ln \left(x \right)\right) \sin \left(\ln \left(x \right)\right)}{2}+\frac{\ln \left(x \right)}{2}"," ",0,"1/2*ln(x)-1/2*cos(ln(x))*sin(ln(x))","A"
141,1,13,12,0.066000," ","int((7-ln(x))/x/(ln(x)+3),x)","-\ln \left(x \right)+10 \ln \left(\ln \left(x \right)+3\right)"," ",0,"-ln(x)+10*ln(ln(x)+3)","A"
142,1,24,17,0.063000," ","int((2-ln(x))*(ln(x)+3)^2/x,x)","-\frac{\ln \left(x \right)^{4}}{4}-\frac{4 \ln \left(x \right)^{3}}{3}+\frac{3 \ln \left(x \right)^{2}}{2}+18 \ln \left(x \right)"," ",0,"-1/4*ln(x)^4-4/3*ln(x)^3+3/2*ln(x)^2+18*ln(x)","A"
143,1,31,32,0.067000," ","int(ln(x)^2*(1+ln(x)^2)^(1/2)/x,x)","-\frac{\arcsinh \left(\ln \left(x \right)\right)}{8}+\frac{\left(\ln \left(x \right)^{2}+1\right)^{\frac{3}{2}} \ln \left(x \right)}{4}-\frac{\sqrt{\ln \left(x \right)^{2}+1}\, \ln \left(x \right)}{8}"," ",0,"1/4*ln(x)*(1+ln(x)^2)^(3/2)-1/8*ln(x)*(1+ln(x)^2)^(1/2)-1/8*arcsinh(ln(x))","A"
144,1,21,20,0.068000," ","int((ln(x)+1)/x/(3+2*ln(x))^2,x)","\frac{\ln \left(2 \ln \left(x \right)+3\right)}{4}+\frac{1}{8 \ln \left(x \right)+12}"," ",0,"1/4/(3+2*ln(x))+1/4*ln(3+2*ln(x))","A"
145,1,18,17,0.066000," ","int(ln(x)/x/(ln(x)+1)^(1/2),x)","\frac{2 \left(\ln \left(x \right)+1\right)^{\frac{3}{2}}}{3}-2 \sqrt{\ln \left(x \right)+1}"," ",0,"2/3*(ln(x)+1)^(3/2)-2*(ln(x)+1)^(1/2)","A"
146,1,22,21,0.069000," ","int(ln(x)/x/(-1+4*ln(x))^(1/2),x)","\frac{\left(4 \ln \left(x \right)-1\right)^{\frac{3}{2}}}{24}+\frac{\sqrt{4 \ln \left(x \right)-1}}{8}"," ",0,"1/24*(-1+4*ln(x))^(3/2)+1/8*(-1+4*ln(x))^(1/2)","A"
147,1,30,18,0.062000," ","int((ln(x)+1)^(1/2)/x/ln(x),x)","-\ln \left(1+\sqrt{\ln \left(x \right)+1}\right)+\ln \left(\sqrt{\ln \left(x \right)+1}-1\right)+2 \sqrt{\ln \left(x \right)+1}"," ",0,"2*(ln(x)+1)^(1/2)+ln((ln(x)+1)^(1/2)-1)-ln(1+(ln(x)+1)^(1/2))","A"
148,1,24,25,0.069000," ","int((1-4*ln(x)+ln(x)^2)/x/(-1+ln(x))^4,x)","-\frac{1}{\ln \left(x \right)-1}+\frac{1}{\left(\ln \left(x \right)-1\right)^{2}}+\frac{2}{3 \left(\ln \left(x \right)-1\right)^{3}}"," ",0,"-1/(-1+ln(x))+1/(-1+ln(x))^2+2/3/(-1+ln(x))^3","A"
149,0,0,27,3.556000," ","int((ln(a*x^n)^2)^p/x,x)","\int \frac{\left(\ln \left(a \,x^{n}\right)^{2}\right)^{p}}{x}\, dx"," ",0,"int((ln(a*x^n)^2)^p/x,x)","F"
150,1,71,27,2.000000," ","int((ln(a*x^n)^m)^p/x,x)","\frac{\left(-\frac{i \pi  \left(\mathrm{csgn}\left(i a \right)-\mathrm{csgn}\left(i a \,x^{n}\right)\right) \left(\mathrm{csgn}\left(i x^{n}\right)-\mathrm{csgn}\left(i a \,x^{n}\right)\right) \mathrm{csgn}\left(i a \,x^{n}\right)}{2}+\ln \left(a \right)+\ln \left(x^{n}\right)\right)^{m p +1}}{\left(m p +1\right) n}"," ",0,"1/n*(ln(a)+ln(x^n)-1/2*I*Pi*csgn(I*a*x^n)*(-csgn(I*a*x^n)+csgn(I*a))*(-csgn(I*a*x^n)+csgn(I*x^n)))^(m*p+1)/(m*p+1)","C"
151,1,21,21,0.353000," ","int((ln(a*x^n)^2)^(1/2)/x,x)","\frac{\mathrm{csgn}\left(\ln \left(a \,x^{n}\right)\right) \ln \left(a \,x^{n}\right)^{2}}{2 n}"," ",0,"1/2/n*csgn(ln(a*x^n))*ln(a*x^n)^2","C"
152,0,0,29,0.711000," ","int((b*ln(a*x^n)^m)^p/x,x)","\int \frac{\left(b \ln \left(a \,x^{n}\right)^{m}\right)^{p}}{x}\, dx"," ",0,"int((b*ln(a*x^n)^m)^p/x,x)","F"
153,1,29,28,0.070000," ","int(1/x/ln(exp(x)),x)","\frac{\ln \left(x \right)}{-x +\ln \left({\mathrm e}^{x}\right)}-\frac{\ln \left(\ln \left({\mathrm e}^{x}\right)\right)}{-x +\ln \left({\mathrm e}^{x}\right)}"," ",0,"-1/(ln(exp(x))-x)*ln(ln(exp(x)))+1/(ln(exp(x))-x)*ln(x)","A"
154,1,80,35,0.977000," ","int(ln(x)*sin(b*x+a),x)","-\frac{\Ei \left(1, -i b x \right) {\mathrm e}^{-i a}}{2 b}-\frac{\Ei \left(1, -i b x \right) {\mathrm e}^{i a}}{2 b}-\frac{i \Si \left(b x \right) {\mathrm e}^{-i a}}{b}-\frac{\cos \left(b x +a \right) \ln \left(x \right)}{b}+\frac{i \pi  \,\mathrm{csgn}\left(b x \right) {\mathrm e}^{-i a}}{2 b}"," ",0,"-cos(b*x+a)*ln(x)/b+1/2*I/b*exp(-I*a)*Pi*csgn(b*x)-I/b*exp(-I*a)*Si(b*x)-1/2/b*exp(-I*a)*Ei(1,-I*b*x)-1/2/b*exp(I*a)*Ei(1,-I*b*x)","C"
155,1,132,56,1.648000," ","int(ln(x)*sin(b*x+a)^2,x)","\frac{x \ln \left(x \right)}{2}+\frac{a \ln \left(i b x \right)}{2 b}-\frac{a \ln \left(a +i \left(i b x +i a \right)\right)}{2 b}-\frac{i \Ei \left(1, -2 i b x \right) {\mathrm e}^{-2 i a}}{8 b}+\frac{i \Ei \left(1, -2 i b x \right) {\mathrm e}^{2 i a}}{8 b}+\frac{\Si \left(2 b x \right) {\mathrm e}^{-2 i a}}{4 b}-\frac{\pi  \,\mathrm{csgn}\left(b x \right) {\mathrm e}^{-2 i a}}{8 b}-\frac{\ln \left(x \right) \sin \left(2 b x +2 a \right)}{4 b}-\frac{x}{2}-\frac{a}{2 b}"," ",0,"1/2*x*ln(x)-1/4*ln(x)/b*sin(2*b*x+2*a)-1/8/b*exp(-2*I*a)*Pi*csgn(b*x)+1/4/b*exp(-2*I*a)*Si(2*b*x)-1/8*I/b*exp(-2*I*a)*Ei(1,-2*I*b*x)+1/2/b*a*ln(I*b*x)-1/2*x-1/2*a/b-1/2/b*a*ln(a+I*(I*b*x+I*a))+1/8*I/b*exp(2*I*a)*Ei(1,-2*I*b*x)","C"
156,1,162,79,1.405000," ","int(ln(x)*sin(b*x+a)^3,x)","\frac{\Ei \left(1, -3 i b x \right) {\mathrm e}^{-3 i a}}{24 b}+\frac{\Ei \left(1, -3 i b x \right) {\mathrm e}^{3 i a}}{24 b}-\frac{3 \Ei \left(1, -i b x \right) {\mathrm e}^{-i a}}{8 b}-\frac{3 \Ei \left(1, -i b x \right) {\mathrm e}^{i a}}{8 b}-\frac{3 i \Si \left(b x \right) {\mathrm e}^{-i a}}{4 b}+\frac{i \Si \left(3 b x \right) {\mathrm e}^{-3 i a}}{12 b}-\frac{3 \cos \left(b x +a \right) \ln \left(x \right)}{4 b}+\frac{\cos \left(3 b x +3 a \right) \ln \left(x \right)}{12 b}-\frac{i \pi  \,\mathrm{csgn}\left(b x \right) {\mathrm e}^{-3 i a}}{24 b}+\frac{3 i \pi  \,\mathrm{csgn}\left(b x \right) {\mathrm e}^{-i a}}{8 b}"," ",0,"-3/4/b*cos(b*x+a)*ln(x)+1/12*ln(x)/b*cos(3*b*x+3*a)-1/24*I/b*exp(-3*I*a)*Pi*csgn(b*x)+1/12*I/b*exp(-3*I*a)*Si(3*b*x)+1/24/b*exp(-3*I*a)*Ei(1,-3*I*b*x)+3/8*I/b*exp(-I*a)*Pi*csgn(b*x)-3/4*I/b*exp(-I*a)*Si(b*x)-3/8/b*exp(-I*a)*Ei(1,-I*b*x)-3/8/b*exp(I*a)*Ei(1,-I*b*x)+1/24/b*exp(3*I*a)*Ei(1,-3*I*b*x)","C"
157,1,79,35,1.111000," ","int(cos(b*x+a)*ln(x),x)","\frac{i \Ei \left(1, -i b x \right) {\mathrm e}^{-i a}}{2 b}-\frac{i \Ei \left(1, -i b x \right) {\mathrm e}^{i a}}{2 b}-\frac{\Si \left(b x \right) {\mathrm e}^{-i a}}{b}+\frac{\pi  \,\mathrm{csgn}\left(b x \right) {\mathrm e}^{-i a}}{2 b}+\frac{\ln \left(x \right) \sin \left(b x +a \right)}{b}"," ",0,"ln(x)*sin(b*x+a)/b+1/2/b*exp(-I*a)*Pi*csgn(b*x)-1/b*exp(-I*a)*Si(b*x)+1/2*I/b*exp(-I*a)*Ei(1,-I*b*x)-1/2*I/b*exp(I*a)*Ei(1,-I*b*x)","C"
158,1,132,56,1.334000," ","int(cos(b*x+a)^2*ln(x),x)","\frac{x \ln \left(x \right)}{2}+\frac{a \ln \left(i b x \right)}{2 b}-\frac{a \ln \left(a +i \left(i b x +i a \right)\right)}{2 b}+\frac{i \Ei \left(1, -2 i b x \right) {\mathrm e}^{-2 i a}}{8 b}-\frac{i \Ei \left(1, -2 i b x \right) {\mathrm e}^{2 i a}}{8 b}-\frac{\Si \left(2 b x \right) {\mathrm e}^{-2 i a}}{4 b}+\frac{\pi  \,\mathrm{csgn}\left(b x \right) {\mathrm e}^{-2 i a}}{8 b}+\frac{\ln \left(x \right) \sin \left(2 b x +2 a \right)}{4 b}-\frac{x}{2}-\frac{a}{2 b}"," ",0,"1/2*x*ln(x)+1/4/b*ln(x)*sin(2*b*x+2*a)+1/8*Pi/b*csgn(b*x)*exp(-2*I*a)-1/4/b*exp(-2*I*a)*Si(2*b*x)+1/8*I/b*exp(-2*I*a)*Ei(1,-2*I*b*x)+1/2*a/b*ln(I*b*x)-1/2*x-1/2*a/b-1/2*a/b*ln(a+I*(I*b*x+I*a))-1/8*I/b*exp(2*I*a)*Ei(1,-2*I*b*x)","C"
159,1,162,78,1.727000," ","int(cos(b*x+a)^3*ln(x),x)","\frac{i \Ei \left(1, -3 i b x \right) {\mathrm e}^{-3 i a}}{24 b}-\frac{i \Ei \left(1, -3 i b x \right) {\mathrm e}^{3 i a}}{24 b}+\frac{3 i \Ei \left(1, -i b x \right) {\mathrm e}^{-i a}}{8 b}-\frac{3 i \Ei \left(1, -i b x \right) {\mathrm e}^{i a}}{8 b}-\frac{3 \Si \left(b x \right) {\mathrm e}^{-i a}}{4 b}-\frac{\Si \left(3 b x \right) {\mathrm e}^{-3 i a}}{12 b}+\frac{\pi  \,\mathrm{csgn}\left(b x \right) {\mathrm e}^{-3 i a}}{24 b}+\frac{3 \pi  \,\mathrm{csgn}\left(b x \right) {\mathrm e}^{-i a}}{8 b}+\frac{3 \ln \left(x \right) \sin \left(b x +a \right)}{4 b}+\frac{\ln \left(x \right) \sin \left(3 b x +3 a \right)}{12 b}"," ",0,"3/4/b*ln(x)*sin(b*x+a)+1/12*ln(x)/b*sin(3*b*x+3*a)+1/24/b*exp(-3*I*a)*Pi*csgn(b*x)-1/12/b*exp(-3*I*a)*Si(3*b*x)+1/24*I/b*exp(-3*I*a)*Ei(1,-3*I*b*x)+3/8*Pi/b*csgn(b*x)*exp(-I*a)-3/4/b*exp(-I*a)*Si(b*x)+3/8*I/b*exp(-I*a)*Ei(1,-I*b*x)-3/8*I/b*exp(I*a)*Ei(1,-I*b*x)-1/24*I/b*exp(3*I*a)*Ei(1,-3*I*b*x)","C"
160,1,19,5,0.934000," ","int(cos(x)*ln(x)+sin(x)/x,x)","\frac{2 \ln \left(x \right) \tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)+1}"," ",0,"2*ln(x)*tan(1/2*x)/(1+tan(1/2*x)^2)","B"
161,1,76,37,0.413000," ","int(ln(a*sin(x)),x)","-i \ln \left(2 a \sin \left(x \right)\right) \ln \left({\mathrm e}^{i x}\right)+i \ln \left({\mathrm e}^{i x}+1\right) \ln \left({\mathrm e}^{i x}\right)-\frac{i \ln \left({\mathrm e}^{i x}\right)^{2}}{2}+i \dilog \left({\mathrm e}^{i x}+1\right)-i \dilog \left({\mathrm e}^{i x}\right)+i \ln \left(2\right) \ln \left({\mathrm e}^{i x}\right)"," ",0,"-I*ln(exp(I*x))*ln(2*a*sin(x))-I*dilog(exp(I*x))+I*ln(exp(I*x))*ln(1+exp(I*x))+I*dilog(1+exp(I*x))-1/2*I*ln(exp(I*x))^2+I*ln(2)*ln(exp(I*x))","B"
162,1,88,39,0.454000," ","int(ln(a*sin(x)^2),x)","-i \ln \left(-\left({\mathrm e}^{2 i x}-1\right)^{2} a \,{\mathrm e}^{-2 i x}\right) \ln \left({\mathrm e}^{i x}\right)+2 i \ln \left({\mathrm e}^{i x}+1\right) \ln \left({\mathrm e}^{i x}\right)-i \ln \left({\mathrm e}^{i x}\right)^{2}+2 i \dilog \left({\mathrm e}^{i x}+1\right)-2 i \dilog \left({\mathrm e}^{i x}\right)+2 i \ln \left(2\right) \ln \left({\mathrm e}^{i x}\right)"," ",0,"2*I*ln(2)*ln(exp(I*x))-I*ln(exp(I*x))^2-I*ln(exp(I*x))*ln(-a*(exp(2*I*x)-1)^2*exp(-2*I*x))+2*I*ln(exp(I*x))*ln(exp(I*x)+1)-2*I*dilog(exp(I*x))+2*I*dilog(exp(I*x)+1)","B"
163,0,0,42,2.075000," ","int(ln(a*sin(x)^n),x)","\int \ln \left(a \left(\sin^{n}\left(x \right)\right)\right)\, dx"," ",0,"int(ln(a*sin(x)^n),x)","F"
164,1,107,37,0.333000," ","int(ln(a*cos(x)),x)","-i \ln \left(2 a \cos \left(x \right)\right) \ln \left({\mathrm e}^{i x}\right)+i \ln \left(-i {\mathrm e}^{i x}+1\right) \ln \left({\mathrm e}^{i x}\right)+i \ln \left(i {\mathrm e}^{i x}+1\right) \ln \left({\mathrm e}^{i x}\right)-\frac{i \ln \left({\mathrm e}^{i x}\right)^{2}}{2}+i \dilog \left(-i {\mathrm e}^{i x}+1\right)+i \dilog \left(i {\mathrm e}^{i x}+1\right)+i \ln \left(2\right) \ln \left({\mathrm e}^{i x}\right)"," ",0,"-I*ln(exp(I*x))*ln(2*a*cos(x))+I*ln(exp(I*x))*ln(1+I*exp(I*x))+I*ln(exp(I*x))*ln(1-I*exp(I*x))+I*dilog(1+I*exp(I*x))+I*dilog(1-I*exp(I*x))-1/2*I*ln(exp(I*x))^2+I*ln(2)*ln(exp(I*x))","B"
165,1,118,39,0.445000," ","int(ln(a*cos(x)^2),x)","-i \ln \left(\left({\mathrm e}^{2 i x}+1\right)^{2} a \,{\mathrm e}^{-2 i x}\right) \ln \left({\mathrm e}^{i x}\right)+2 i \ln \left(-i {\mathrm e}^{i x}+1\right) \ln \left({\mathrm e}^{i x}\right)+2 i \ln \left(i {\mathrm e}^{i x}+1\right) \ln \left({\mathrm e}^{i x}\right)-i \ln \left({\mathrm e}^{i x}\right)^{2}+2 i \dilog \left(-i {\mathrm e}^{i x}+1\right)+2 i \dilog \left(i {\mathrm e}^{i x}+1\right)+2 i \ln \left(2\right) \ln \left({\mathrm e}^{i x}\right)"," ",0,"2*I*ln(2)*ln(exp(I*x))-I*ln(exp(I*x))^2-I*ln(exp(I*x))*ln(a*(1+exp(2*I*x))^2*exp(-2*I*x))+2*I*ln(exp(I*x))*ln(I*exp(I*x)+1)+2*I*ln(exp(I*x))*ln(-I*exp(I*x)+1)+2*I*dilog(-I*exp(I*x)+1)+2*I*dilog(I*exp(I*x)+1)","B"
166,0,0,42,1.611000," ","int(ln(a*cos(x)^n),x)","\int \ln \left(a \left(\cos^{n}\left(x \right)\right)\right)\, dx"," ",0,"int(ln(a*cos(x)^n),x)","F"
167,1,82,39,0.168000," ","int(ln(a*tan(x)),x)","-\frac{i \ln \left(a \tan \left(x \right)\right) \ln \left(\frac{i a \tan \left(x \right)+a}{a}\right)}{2}+\frac{i \ln \left(a \tan \left(x \right)\right) \ln \left(-\frac{i a \tan \left(x \right)-a}{a}\right)}{2}-\frac{i \dilog \left(\frac{i a \tan \left(x \right)+a}{a}\right)}{2}+\frac{i \dilog \left(-\frac{i a \tan \left(x \right)-a}{a}\right)}{2}"," ",0,"-1/2*I*ln(a*tan(x))*ln((I*a*tan(x)+a)/a)+1/2*I*ln(a*tan(x))*ln(-(I*a*tan(x)-a)/a)-1/2*I*dilog((I*a*tan(x)+a)/a)+1/2*I*dilog(-(I*a*tan(x)-a)/a)","B"
168,1,82,41,0.566000," ","int(ln(a*tan(x)^2),x)","i \ln \left(-i \tan \left(x \right)\right) \ln \left(\tan \left(x \right)-i\right)-i \ln \left(i \tan \left(x \right)\right) \ln \left(\tan \left(x \right)+i\right)-\frac{i \ln \left(a \left(\tan^{2}\left(x \right)\right)\right) \ln \left(\tan \left(x \right)-i\right)}{2}+\frac{i \ln \left(a \left(\tan^{2}\left(x \right)\right)\right) \ln \left(\tan \left(x \right)+i\right)}{2}+i \dilog \left(-i \tan \left(x \right)\right)-i \dilog \left(i \tan \left(x \right)\right)"," ",0,"I*ln(tan(x)-I)*ln(-I*tan(x))-1/2*I*ln(tan(x)-I)*ln(a*tan(x)^2)+I*dilog(-I*tan(x))+1/2*I*ln(a*tan(x)^2)*ln(tan(x)+I)-I*ln(tan(x)+I)*ln(I*tan(x))-I*dilog(I*tan(x))","A"
169,-1,0,44,180.000000," ","int(ln(a*tan(x)^n),x)","\int \ln \left(a \left(\tan^{n}\left(x \right)\right)\right)\, dx"," ",0,"int(ln(a*tan(x)^n),x)","F"
170,1,82,39,0.157000," ","int(ln(a*cot(x)),x)","\frac{i \ln \left(a \cot \left(x \right)\right) \ln \left(\frac{i a \cot \left(x \right)+a}{a}\right)}{2}-\frac{i \ln \left(a \cot \left(x \right)\right) \ln \left(-\frac{i a \cot \left(x \right)-a}{a}\right)}{2}+\frac{i \dilog \left(\frac{i a \cot \left(x \right)+a}{a}\right)}{2}-\frac{i \dilog \left(-\frac{i a \cot \left(x \right)-a}{a}\right)}{2}"," ",0,"1/2*I*ln(a*cot(x))*ln((I*a*cot(x)+a)/a)-1/2*I*ln(a*cot(x))*ln(-(I*a*cot(x)-a)/a)+1/2*I*dilog((I*a*cot(x)+a)/a)-1/2*I*dilog(-(I*a*cot(x)-a)/a)","B"
171,1,82,41,0.461000," ","int(ln(a*cot(x)^2),x)","-i \ln \left(-i \cot \left(x \right)\right) \ln \left(\cot \left(x \right)-i\right)+i \ln \left(i \cot \left(x \right)\right) \ln \left(\cot \left(x \right)+i\right)+\frac{i \ln \left(a \left(\cot^{2}\left(x \right)\right)\right) \ln \left(\cot \left(x \right)-i\right)}{2}-\frac{i \ln \left(a \left(\cot^{2}\left(x \right)\right)\right) \ln \left(\cot \left(x \right)+i\right)}{2}-i \dilog \left(-i \cot \left(x \right)\right)+i \dilog \left(i \cot \left(x \right)\right)"," ",0,"1/2*I*ln(a*cot(x)^2)*ln(cot(x)-I)-I*ln(cot(x)-I)*ln(-I*cot(x))-I*dilog(-I*cot(x))-1/2*I*ln(a*cot(x)^2)*ln(cot(x)+I)+I*ln(cot(x)+I)*ln(I*cot(x))+I*dilog(I*cot(x))","A"
172,-1,0,44,180.000000," ","int(ln(a*cot(x)^n),x)","\int \ln \left(a \left(\cot^{n}\left(x \right)\right)\right)\, dx"," ",0,"int(ln(a*cot(x)^n),x)","F"
173,1,118,36,0.536000," ","int(ln(a*sec(x)),x)","-i \ln \left(\frac{a \,{\mathrm e}^{i x}}{{\mathrm e}^{2 i x}+1}\right) \ln \left({\mathrm e}^{i x}\right)-i \ln \left(-i {\mathrm e}^{i x}+1\right) \ln \left({\mathrm e}^{i x}\right)-i \ln \left(i {\mathrm e}^{i x}+1\right) \ln \left({\mathrm e}^{i x}\right)+\frac{i \ln \left({\mathrm e}^{i x}\right)^{2}}{2}-i \dilog \left(-i {\mathrm e}^{i x}+1\right)-i \dilog \left(i {\mathrm e}^{i x}+1\right)-i \ln \left(2\right) \ln \left({\mathrm e}^{i x}\right)"," ",0,"-I*ln(2)*ln(exp(I*x))-I*ln(exp(I*x))*ln(a*exp(I*x)/(exp(2*I*x)+1))-I*ln(exp(I*x))*ln(I*exp(I*x)+1)-I*ln(exp(I*x))*ln(-I*exp(I*x)+1)-I*dilog(I*exp(I*x)+1)-I*dilog(-I*exp(I*x)+1)+1/2*I*ln(exp(I*x))^2","B"
174,1,118,39,0.491000," ","int(ln(a*sec(x)^2),x)","-i \ln \left(\frac{a \,{\mathrm e}^{2 i x}}{\left({\mathrm e}^{2 i x}+1\right)^{2}}\right) \ln \left({\mathrm e}^{i x}\right)-2 i \ln \left(-i {\mathrm e}^{i x}+1\right) \ln \left({\mathrm e}^{i x}\right)-2 i \ln \left(i {\mathrm e}^{i x}+1\right) \ln \left({\mathrm e}^{i x}\right)+i \ln \left({\mathrm e}^{i x}\right)^{2}-2 i \dilog \left(-i {\mathrm e}^{i x}+1\right)-2 i \dilog \left(i {\mathrm e}^{i x}+1\right)-2 i \ln \left(2\right) \ln \left({\mathrm e}^{i x}\right)"," ",0,"-I*ln(a*exp(2*I*x)/(exp(2*I*x)+1)^2)*ln(exp(I*x))-2*I*ln(I*exp(I*x)+1)*ln(exp(I*x))-2*I*ln(-I*exp(I*x)+1)*ln(exp(I*x))+I*ln(exp(I*x))^2-2*I*ln(exp(I*x))*ln(2)-2*I*dilog(I*exp(I*x)+1)-2*I*dilog(-I*exp(I*x)+1)","B"
175,0,0,41,1.614000," ","int(ln(a*sec(x)^n),x)","\int \ln \left(a \left(\sec^{n}\left(x \right)\right)\right)\, dx"," ",0,"int(ln(a*sec(x)^n),x)","F"
176,1,89,36,0.492000," ","int(ln(a*csc(x)),x)","-i \ln \left(\frac{i a \,{\mathrm e}^{i x}}{{\mathrm e}^{2 i x}-1}\right) \ln \left({\mathrm e}^{i x}\right)-i \ln \left({\mathrm e}^{i x}+1\right) \ln \left({\mathrm e}^{i x}\right)+\frac{i \ln \left({\mathrm e}^{i x}\right)^{2}}{2}-i \dilog \left({\mathrm e}^{i x}+1\right)+i \dilog \left({\mathrm e}^{i x}\right)-i \ln \left(2\right) \ln \left({\mathrm e}^{i x}\right)"," ",0,"-I*ln(2)*ln(exp(I*x))-I*ln(exp(I*x))*ln(I*a*exp(I*x)/(exp(2*I*x)-1))+I*dilog(exp(I*x))-I*ln(exp(I*x))*ln(exp(I*x)+1)-I*dilog(exp(I*x)+1)+1/2*I*ln(exp(I*x))^2","B"
177,1,88,39,0.553000," ","int(ln(a*csc(x)^2),x)","-i \ln \left(-\frac{a \,{\mathrm e}^{2 i x}}{\left({\mathrm e}^{2 i x}-1\right)^{2}}\right) \ln \left({\mathrm e}^{i x}\right)-2 i \ln \left({\mathrm e}^{i x}+1\right) \ln \left({\mathrm e}^{i x}\right)+i \ln \left({\mathrm e}^{i x}\right)^{2}-2 i \dilog \left({\mathrm e}^{i x}+1\right)+2 i \dilog \left({\mathrm e}^{i x}\right)-2 i \ln \left(2\right) \ln \left({\mathrm e}^{i x}\right)"," ",0,"-I*ln(-a*exp(2*I*x)/(exp(2*I*x)-1)^2)*ln(exp(I*x))-2*I*ln(exp(I*x)+1)*ln(exp(I*x))+I*ln(exp(I*x))^2-2*I*ln(2)*ln(exp(I*x))+2*I*dilog(exp(I*x))-2*I*dilog(exp(I*x)+1)","B"
178,0,0,41,2.099000," ","int(ln(a*csc(x)^n),x)","\int \ln \left(a \left(\csc^{n}\left(x \right)\right)\right)\, dx"," ",0,"int(ln(a*csc(x)^n),x)","F"
179,1,72,17,0.603000," ","int(cos(x)*ln(1/2-1/2*cos(2*x)),x)","\frac{i {\mathrm e}^{-i x} \ln \left(-2 \cos \left(2 x \right)+2\right)}{2}-\frac{i {\mathrm e}^{i x} \ln \left(-2 \cos \left(2 x \right)+2\right)}{2}-i \ln \left(2\right) {\mathrm e}^{-i x}-i {\mathrm e}^{-i x}+i \ln \left(2\right) {\mathrm e}^{i x}+i {\mathrm e}^{i x}"," ",0,"I*ln(2)*exp(I*x)-I*ln(2)*exp(-I*x)-1/2*I*exp(I*x)*ln(2-2*cos(2*x))+1/2*I*exp(-I*x)*ln(2-2*cos(2*x))+I*exp(I*x)-I*exp(-I*x)","C"
180,1,7,6,0.401000," ","int(cot(x)/ln(E*sin(x)),x)","\ln \left(\ln \left(E \sin \left(x \right)\right)\right)"," ",0,"ln(ln(E*sin(x)))","A"
181,1,35,34,0.450000," ","int(cot(x)/ln(exp(sin(x))),x)","-\frac{\ln \left(\ln \left({\mathrm e}^{\sin \left(x \right)}\right)\right)}{\ln \left({\mathrm e}^{\sin \left(x \right)}\right)-\sin \left(x \right)}+\frac{\ln \left(\sin \left(x \right)\right)}{\ln \left({\mathrm e}^{\sin \left(x \right)}\right)-\sin \left(x \right)}"," ",0,"-1/(ln(exp(sin(x)))-sin(x))*ln(ln(exp(sin(x))))+1/(ln(exp(sin(x)))-sin(x))*ln(sin(x))","A"
182,1,61,12,0.582000," ","int(ln(cos(x))*sec(x)^2,x)","-\frac{2 i {\mathrm e}^{2 i x} \ln \left(2 \cos \left(x \right)\right)}{{\mathrm e}^{2 i x}+1}+i \ln \left({\mathrm e}^{2 i x}+1\right)+\frac{2 i}{{\mathrm e}^{2 i x}+1}-\frac{2 i \ln \left(2\right)}{{\mathrm e}^{2 i x}+1}"," ",0,"-2*I/(exp(2*I*x)+1)*exp(2*I*x)*ln(2*cos(x))+2*I/(exp(2*I*x)+1)+I*ln(exp(2*I*x)+1)-2*I*ln(2)/(exp(2*I*x)+1)","C"
183,1,8,7,0.190000," ","int(cot(x)*ln(sin(x)),x)","\frac{\ln \left(\sin \left(x \right)\right)^{2}}{2}"," ",0,"1/2*ln(sin(x))^2","A"
184,1,17,16,0.073000," ","int(cos(x)*ln(sin(x))*sin(x)^2,x)","\frac{\ln \left(\sin \left(x \right)\right) \left(\sin^{3}\left(x \right)\right)}{3}-\frac{\left(\sin^{3}\left(x \right)\right)}{9}"," ",0,"-1/9*sin(x)^3+1/3*ln(sin(x))*sin(x)^3","A"
185,1,32,42,0.737000," ","int(cos(b*x+a)*ln(cos(1/2*b*x+1/2*a)*sin(1/2*b*x+1/2*a)),x)","\frac{\ln \left(\frac{\sin \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{b}-\frac{\sin \left(b x +a \right)}{b}"," ",0,"ln(1/2*sin(b*x+a))/b*sin(b*x+a)-sin(b*x+a)/b","A"
186,1,7,6,0.305000," ","int(tan(x)/ln(cos(x)),x)","-\ln \left(\ln \left(\cos \left(x \right)\right)\right)"," ",0,"-ln(ln(cos(x)))","A"
187,1,8,7,0.189000," ","int(ln(cos(x))*tan(x),x)","-\frac{\ln \left(\cos \left(x \right)\right)^{2}}{2}"," ",0,"-1/2*ln(cos(x))^2","A"
188,1,11,10,0.182000," ","int(ln(cos(x))*sin(x),x)","-\cos \left(x \right) \ln \left(\cos \left(x \right)\right)+\cos \left(x \right)"," ",0,"cos(x)-cos(x)*ln(cos(x))","A"
189,1,73,14,0.313000," ","int(cos(x)*ln(cos(x)),x)","\frac{i {\mathrm e}^{-i x} \ln \left(2 \cos \left(x \right)\right)}{2}-\frac{i {\mathrm e}^{i x} \ln \left(2 \cos \left(x \right)\right)}{2}-2 i \arctan \left({\mathrm e}^{i x}\right)-\frac{i \ln \left(2\right) {\mathrm e}^{-i x}}{2}-\frac{i {\mathrm e}^{-i x}}{2}+\frac{i \ln \left(2\right) {\mathrm e}^{i x}}{2}+\frac{i {\mathrm e}^{i x}}{2}"," ",0,"-1/2*I*ln(2)*exp(-I*x)+1/2*I*ln(2)*exp(I*x)+1/2*I*exp(-I*x)*ln(2*cos(x))-1/2*I*ln(2*cos(x))*exp(I*x)-1/2*I*exp(-I*x)-2*I*arctan(exp(I*x))+1/2*I*exp(I*x)","C"
190,1,12,11,0.186000," ","int(cos(x)*ln(sin(x)),x)","\ln \left(\sin \left(x \right)\right) \sin \left(x \right)-\sin \left(x \right)"," ",0,"-sin(x)+ln(sin(x))*sin(x)","A"
191,1,146,54,0.330000," ","int(ln(sin(x))*sin(x)^2,x)","-\frac{i {\mathrm e}^{-2 i x} \ln \left(2 \sin \left(x \right)\right)}{8}+\frac{i {\mathrm e}^{2 i x} \ln \left(2 \sin \left(x \right)\right)}{8}-\frac{i \ln \left(2 \sin \left(x \right)\right) \ln \left({\mathrm e}^{i x}\right)}{2}+\frac{i \ln \left({\mathrm e}^{i x}+1\right) \ln \left({\mathrm e}^{i x}\right)}{2}-\frac{i \ln \left({\mathrm e}^{i x}\right)^{2}}{4}+\frac{i \dilog \left({\mathrm e}^{i x}+1\right)}{2}-\frac{i \dilog \left({\mathrm e}^{i x}\right)}{2}+\frac{i {\mathrm e}^{-2 i x}}{16}+\frac{i \ln \left(2\right) {\mathrm e}^{-2 i x}}{8}-\frac{i {\mathrm e}^{2 i x}}{16}-\frac{i \ln \left(2\right) {\mathrm e}^{2 i x}}{8}-\frac{i \ln \left({\mathrm e}^{i x}\right)}{4}+\frac{i \ln \left(2\right) \ln \left({\mathrm e}^{i x}\right)}{2}"," ",0,"1/8*I*ln(2*sin(x))*exp(2*I*x)-1/16*I*exp(2*I*x)-1/2*I*ln(exp(I*x))*ln(2*sin(x))-1/4*I*ln(exp(I*x))^2+1/2*I*ln(exp(I*x))*ln(exp(I*x)+1)-1/2*I*dilog(exp(I*x))+1/2*I*dilog(exp(I*x)+1)-1/8*I*exp(-2*I*x)*ln(2*sin(x))+1/16*I*exp(-2*I*x)-1/4*I*ln(exp(I*x))-1/8*I*ln(2)*exp(2*I*x)+1/8*I*ln(2)*exp(-2*I*x)+1/2*I*ln(2)*ln(exp(I*x))","B"
192,1,134,32,0.342000," ","int(ln(sin(x))*sin(x)^3,x)","\frac{{\mathrm e}^{-3 i x} \ln \left(2 \sin \left(x \right)\right)}{24}-\frac{3 \,{\mathrm e}^{-i x} \ln \left(2 \sin \left(x \right)\right)}{8}-\frac{3 \,{\mathrm e}^{i x} \ln \left(2 \sin \left(x \right)\right)}{8}+\frac{{\mathrm e}^{3 i x} \ln \left(2 \sin \left(x \right)\right)}{24}-\frac{{\mathrm e}^{-3 i x}}{72}-\frac{\ln \left(2\right) {\mathrm e}^{-3 i x}}{24}+\frac{7 \,{\mathrm e}^{-i x}}{24}+\frac{3 \ln \left(2\right) {\mathrm e}^{-i x}}{8}+\frac{7 \,{\mathrm e}^{i x}}{24}+\frac{3 \ln \left(2\right) {\mathrm e}^{i x}}{8}-\frac{{\mathrm e}^{3 i x}}{72}-\frac{\ln \left(2\right) {\mathrm e}^{3 i x}}{24}-\frac{2 \ln \left({\mathrm e}^{i x}+1\right)}{3}+\frac{2 \ln \left({\mathrm e}^{i x}-1\right)}{3}"," ",0,"1/24*exp(3*I*x)*ln(2*sin(x))-1/72*exp(3*I*x)+7/24*exp(I*x)+2/3*ln(exp(I*x)-1)-2/3*ln(exp(I*x)+1)-3/8*exp(I*x)*ln(2*sin(x))-3/8*exp(-I*x)*ln(2*sin(x))+7/24*exp(-I*x)+1/24*exp(-3*I*x)*ln(2*sin(x))-1/72*exp(-3*I*x)-1/24*ln(2)*exp(3*I*x)+3/8*ln(2)*exp(I*x)+3/8*ln(2)*exp(-I*x)-1/24*ln(2)*exp(-3*I*x)","C"
193,0,0,55,0.299000," ","int(ln(sin(x^(1/2))),x)","\int \ln \left(\sin \left(\sqrt{x}\right)\right)\, dx"," ",0,"int(ln(sin(x^(1/2))),x)","F"
194,1,72,15,0.724000," ","int(csc(x)^2*ln(sin(x)),x)","-\frac{2 i {\mathrm e}^{2 i x} \ln \left(2 \sin \left(x \right)\right)}{{\mathrm e}^{2 i x}-1}+i \ln \left({\mathrm e}^{i x}+1\right)+i \ln \left({\mathrm e}^{i x}-1\right)-\frac{2 i}{{\mathrm e}^{2 i x}-1}+\frac{2 i \ln \left(2\right)}{{\mathrm e}^{2 i x}-1}"," ",0,"-2*I/(exp(2*I*x)-1)*ln(2*sin(x))*exp(2*I*x)-2*I/(exp(2*I*x)-1)+I*ln(exp(I*x)-1)+I*ln(exp(I*x)+1)+2*I*ln(2)/(exp(2*I*x)-1)","C"
195,1,58,35,0.704000," ","int(ln(x)*sinh(b*x+a),x)","\frac{\Ei \left(1, b x \right) {\mathrm e}^{-a}}{2 b}+\frac{\Ei \left(1, -b x \right) {\mathrm e}^{a}}{2 b}+\left(\frac{{\mathrm e}^{-b x -a}}{2 b}+\frac{{\mathrm e}^{b x +a}}{2 b}\right) \ln \left(x \right)"," ",0,"(1/2/b*exp(b*x+a)+1/2*exp(-b*x-a)/b)*ln(x)+1/2/b*exp(-a)*Ei(1,b*x)+1/2/b*exp(a)*Ei(1,-b*x)","A"
196,1,97,56,1.303000," ","int(ln(x)*sinh(b*x+a)^2,x)","-\frac{a \ln \left(b x \right)}{2 b}+\frac{a \ln \left(-b x \right)}{2 b}+\frac{\Ei \left(1, -2 b x \right) {\mathrm e}^{2 a}}{8 b}-\frac{\Ei \left(1, 2 b x \right) {\mathrm e}^{-2 a}}{8 b}+\frac{x}{2}+\left(-\frac{x}{2}-\frac{{\mathrm e}^{-2 b x -2 a}}{8 b}+\frac{{\mathrm e}^{2 b x +2 a}}{8 b}\right) \ln \left(x \right)+\frac{a}{2 b}"," ",0,"(-1/2*x+1/8/b*exp(2*b*x+2*a)-1/8/b*exp(-2*b*x-2*a))*ln(x)+1/8/b*exp(2*a)*Ei(1,-2*b*x)-1/2/b*a*ln(b*x)+1/2/b*a*ln(-b*x)+1/2*x+1/2*a/b-1/8/b*exp(-2*a)*Ei(1,2*b*x)","A"
197,1,116,79,1.043000," ","int(ln(x)*sinh(b*x+a)^3,x)","-\frac{3 \Ei \left(1, b x \right) {\mathrm e}^{-a}}{8 b}+\frac{\Ei \left(1, -3 b x \right) {\mathrm e}^{3 a}}{24 b}-\frac{3 \Ei \left(1, -b x \right) {\mathrm e}^{a}}{8 b}+\frac{\Ei \left(1, 3 b x \right) {\mathrm e}^{-3 a}}{24 b}+\left(\frac{{\mathrm e}^{-3 b x -3 a}}{24 b}-\frac{3 \,{\mathrm e}^{-b x -a}}{8 b}-\frac{3 \,{\mathrm e}^{b x +a}}{8 b}+\frac{{\mathrm e}^{3 b x +3 a}}{24 b}\right) \ln \left(x \right)"," ",0,"(1/24/b*exp(3*b*x+3*a)-3/8/b*exp(b*x+a)-3/8/b*exp(-b*x-a)+1/24/b*exp(-3*b*x-3*a))*ln(x)+1/24/b*exp(-3*a)*Ei(1,3*b*x)+1/24/b*exp(3*a)*Ei(1,-3*b*x)-3/8/b*exp(-a)*Ei(1,b*x)-3/8/b*exp(a)*Ei(1,-b*x)","A"
198,1,58,35,0.935000," ","int(cosh(b*x+a)*ln(x),x)","-\frac{\Ei \left(1, b x \right) {\mathrm e}^{-a}}{2 b}+\frac{\Ei \left(1, -b x \right) {\mathrm e}^{a}}{2 b}+\left(-\frac{{\mathrm e}^{-b x -a}}{2 b}+\frac{{\mathrm e}^{b x +a}}{2 b}\right) \ln \left(x \right)"," ",0,"(1/2/b*exp(b*x+a)-1/2/b*exp(-b*x-a))*ln(x)+1/2/b*exp(a)*Ei(1,-b*x)-1/2/b*exp(-a)*Ei(1,b*x)","A"
199,1,97,56,1.239000," ","int(cosh(b*x+a)^2*ln(x),x)","\frac{a \ln \left(b x \right)}{2 b}-\frac{a \ln \left(-b x \right)}{2 b}+\frac{\Ei \left(1, -2 b x \right) {\mathrm e}^{2 a}}{8 b}-\frac{\Ei \left(1, 2 b x \right) {\mathrm e}^{-2 a}}{8 b}-\frac{x}{2}+\left(\frac{x}{2}-\frac{{\mathrm e}^{-2 b x -2 a}}{8 b}+\frac{{\mathrm e}^{2 b x +2 a}}{8 b}\right) \ln \left(x \right)-\frac{a}{2 b}"," ",0,"(1/2*x+1/8/b*exp(2*b*x+2*a)-1/8/b*exp(-2*b*x-2*a))*ln(x)+1/8/b*exp(2*a)*Ei(1,-2*b*x)+1/2*a/b*ln(b*x)-1/2*a/b*ln(-b*x)-1/2*x-1/2*a/b-1/8/b*exp(-2*a)*Ei(1,2*b*x)","A"
200,1,116,78,1.690000," ","int(cosh(b*x+a)^3*ln(x),x)","-\frac{3 \Ei \left(1, b x \right) {\mathrm e}^{-a}}{8 b}+\frac{\Ei \left(1, -3 b x \right) {\mathrm e}^{3 a}}{24 b}+\frac{3 \Ei \left(1, -b x \right) {\mathrm e}^{a}}{8 b}-\frac{\Ei \left(1, 3 b x \right) {\mathrm e}^{-3 a}}{24 b}+\left(-\frac{{\mathrm e}^{-3 b x -3 a}}{24 b}-\frac{3 \,{\mathrm e}^{-b x -a}}{8 b}+\frac{3 \,{\mathrm e}^{b x +a}}{8 b}+\frac{{\mathrm e}^{3 b x +3 a}}{24 b}\right) \ln \left(x \right)"," ",0,"(1/24/b*exp(3*b*x+3*a)+3/8/b*exp(b*x+a)-3/8/b*exp(-b*x-a)-1/24/b*exp(-3*b*x-3*a))*ln(x)+1/24/b*exp(3*a)*Ei(1,-3*b*x)-1/24/b*exp(-3*a)*Ei(1,3*b*x)-3/8/b*exp(-a)*Ei(1,b*x)+3/8/b*exp(a)*Ei(1,-b*x)","A"
201,1,295,33,0.990000," ","int(ln(a*sinh(x)),x)","-\frac{i \pi  x \,\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right) {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right) a \,{\mathrm e}^{-x}\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right) a \,{\mathrm e}^{-x}\right)^{2}}{2}-\frac{i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right) {\mathrm e}^{-x}\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right) {\mathrm e}^{-x}\right)^{2}}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right) {\mathrm e}^{-x}\right)^{2}}{2}-\frac{i \pi  x \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right) {\mathrm e}^{-x}\right)^{3}}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right) {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right) a \,{\mathrm e}^{-x}\right)^{2}}{2}-\frac{i \pi  x \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right) a \,{\mathrm e}^{-x}\right)^{3}}{2}+\frac{x^{2}}{2}+x \ln \left(a \right)-x \ln \left({\mathrm e}^{x}\right)+\ln \left({\mathrm e}^{2 x}-1\right) \ln \left({\mathrm e}^{x}\right)-\ln \left({\mathrm e}^{x}+1\right) \ln \left({\mathrm e}^{x}\right)-\ln \left(2\right) x -\dilog \left({\mathrm e}^{x}+1\right)+\dilog \left({\mathrm e}^{x}\right)"," ",0,"-x*ln(exp(x))+1/2*I*Pi*csgn(I*(exp(2*x)-1))*csgn(I*exp(-x)*(exp(2*x)-1))^2*x+1/2*I*Pi*csgn(I*a)*csgn(I*a*(exp(2*x)-1)*exp(-x))^2*x-1/2*I*Pi*csgn(I*exp(-x)*(exp(2*x)-1))^3*x+1/2*I*Pi*csgn(I*exp(-x))*csgn(I*exp(-x)*(exp(2*x)-1))^2*x-1/2*I*Pi*csgn(I*a*(exp(2*x)-1)*exp(-x))^3*x-1/2*I*Pi*csgn(I*(exp(2*x)-1))*csgn(I*exp(-x))*csgn(I*exp(-x)*(exp(2*x)-1))*x-ln(2)*x+x*ln(a)+1/2*x^2+1/2*I*Pi*csgn(I*exp(-x)*(exp(2*x)-1))*csgn(I*a*(exp(2*x)-1)*exp(-x))^2*x-1/2*I*Pi*csgn(I*a)*csgn(I*exp(-x)*(exp(2*x)-1))*csgn(I*a*(exp(2*x)-1)*exp(-x))*x+ln(exp(x))*ln(exp(2*x)-1)+dilog(exp(x))-dilog(exp(x)+1)-ln(exp(x))*ln(exp(x)+1)","C"
202,1,454,33,2.237000," ","int(ln(a*sinh(x)^2),x)","-\frac{i \pi  x \,\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)^{2} {\mathrm e}^{-2 x}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)^{2} a \,{\mathrm e}^{-2 x}\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)^{2} a \,{\mathrm e}^{-2 x}\right)^{2}}{2}-\frac{i \pi  x \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)\right)^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)^{2}\right)}{2}+i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)^{2}\right)^{2}-\frac{i \pi  x \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)^{2}\right)^{3}}{2}-\frac{i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)^{2}\right) \mathrm{csgn}\left(i {\mathrm e}^{-2 x}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)^{2} {\mathrm e}^{-2 x}\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)^{2}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)^{2} {\mathrm e}^{-2 x}\right)^{2}}{2}+\frac{i \pi  x \mathrm{csgn}\left(i {\mathrm e}^{x}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{2 x}\right)}{2}-i \pi  x \,\mathrm{csgn}\left(i {\mathrm e}^{x}\right) \mathrm{csgn}\left(i {\mathrm e}^{2 x}\right)^{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i {\mathrm e}^{-2 x}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)^{2} {\mathrm e}^{-2 x}\right)^{2}}{2}+\frac{i \pi  x \mathrm{csgn}\left(i {\mathrm e}^{2 x}\right)^{3}}{2}-\frac{i \pi  x \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)^{2} {\mathrm e}^{-2 x}\right)^{3}}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)^{2} {\mathrm e}^{-2 x}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)^{2} a \,{\mathrm e}^{-2 x}\right)^{2}}{2}-\frac{i \pi  x \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)^{2} a \,{\mathrm e}^{-2 x}\right)^{3}}{2}+x^{2}+x \ln \left(a \right)-2 x \ln \left({\mathrm e}^{x}\right)+2 \ln \left({\mathrm e}^{2 x}-1\right) \ln \left({\mathrm e}^{x}\right)-2 \ln \left({\mathrm e}^{x}+1\right) \ln \left({\mathrm e}^{x}\right)-2 \ln \left(2\right) x -2 \dilog \left({\mathrm e}^{x}+1\right)+2 \dilog \left({\mathrm e}^{x}\right)"," ",0,"-2*ln(2)*x+1/2*I*Pi*csgn(I*(exp(2*x)-1)^2)*csgn(I*exp(-2*x)*(exp(2*x)-1)^2)^2*x+1/2*I*Pi*csgn(I*exp(x))^2*csgn(I*exp(2*x))*x+x*ln(a)+x^2+1/2*I*Pi*csgn(I*exp(-2*x)*(exp(2*x)-1)^2)*csgn(I*a*(exp(2*x)-1)^2*exp(-2*x))^2*x-1/2*I*Pi*csgn(I*(exp(2*x)-1)^2)*csgn(I*exp(-2*x))*csgn(I*exp(-2*x)*(exp(2*x)-1)^2)*x+1/2*I*Pi*csgn(I*exp(-2*x))*csgn(I*exp(-2*x)*(exp(2*x)-1)^2)^2*x+1/2*I*Pi*csgn(I*exp(2*x))^3*x+2*dilog(exp(x))-2*dilog(exp(x)+1)-2*ln(exp(x)+1)*ln(exp(x))-2*x*ln(exp(x))+2*ln(exp(2*x)-1)*ln(exp(x))-1/2*I*Pi*csgn(I*a*(exp(2*x)-1)^2*exp(-2*x))^3*x-I*Pi*csgn(I*exp(x))*csgn(I*exp(2*x))^2*x-1/2*I*Pi*csgn(I*(exp(2*x)-1)^2)^3*x-1/2*I*Pi*csgn(I*exp(-2*x)*(exp(2*x)-1)^2)^3*x-1/2*I*Pi*csgn(I*a)*csgn(I*exp(-2*x)*(exp(2*x)-1)^2)*csgn(I*a*(exp(2*x)-1)^2*exp(-2*x))*x+1/2*I*Pi*csgn(I*a)*csgn(I*a*(exp(2*x)-1)^2*exp(-2*x))^2*x+I*Pi*csgn(I*(exp(2*x)-1))*csgn(I*(exp(2*x)-1)^2)^2*x-1/2*I*Pi*csgn(I*(exp(2*x)-1))^2*csgn(I*(exp(2*x)-1)^2)*x","C"
203,0,0,38,2.091000," ","int(ln(a*sinh(x)^n),x)","\int \ln \left(a \left(\sinh^{n}\left(x \right)\right)\right)\, dx"," ",0,"int(ln(a*sinh(x)^n),x)","F"
204,1,321,33,1.042000," ","int(ln(a*cosh(x)),x)","-\frac{i \pi  x \,\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right) {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right) a \,{\mathrm e}^{-x}\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right) a \,{\mathrm e}^{-x}\right)^{2}}{2}-\frac{i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right) {\mathrm e}^{-x}\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right) {\mathrm e}^{-x}\right)^{2}}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right) {\mathrm e}^{-x}\right)^{2}}{2}-\frac{i \pi  x \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right) {\mathrm e}^{-x}\right)^{3}}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right) {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right) a \,{\mathrm e}^{-x}\right)^{2}}{2}-\frac{i \pi  x \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right) a \,{\mathrm e}^{-x}\right)^{3}}{2}+\frac{x^{2}}{2}+x \ln \left(a \right)-x \ln \left({\mathrm e}^{x}\right)-\ln \left(-i {\mathrm e}^{x}+1\right) \ln \left({\mathrm e}^{x}\right)-\ln \left(i {\mathrm e}^{x}+1\right) \ln \left({\mathrm e}^{x}\right)+\ln \left({\mathrm e}^{2 x}+1\right) \ln \left({\mathrm e}^{x}\right)-\ln \left(2\right) x -\dilog \left(-i {\mathrm e}^{x}+1\right)-\dilog \left(i {\mathrm e}^{x}+1\right)"," ",0,"-x*ln(exp(x))-1/2*I*Pi*csgn(I*a*(exp(2*x)+1)*exp(-x))^3*x+1/2*I*Pi*csgn(I*(exp(2*x)+1))*csgn(I*exp(-x)*(exp(2*x)+1))^2*x-1/2*I*Pi*csgn(I*a)*csgn(I*exp(-x)*(exp(2*x)+1))*csgn(I*a*(exp(2*x)+1)*exp(-x))*x+1/2*I*Pi*csgn(I*exp(-x)*(exp(2*x)+1))*csgn(I*a*(exp(2*x)+1)*exp(-x))^2*x+1/2*I*Pi*csgn(I*exp(-x))*csgn(I*exp(-x)*(exp(2*x)+1))^2*x+1/2*I*Pi*csgn(I*a)*csgn(I*a*(exp(2*x)+1)*exp(-x))^2*x+x*ln(a)-ln(2)*x+1/2*x^2-1/2*I*Pi*csgn(I*exp(-x))*csgn(I*(exp(2*x)+1))*csgn(I*exp(-x)*(exp(2*x)+1))*x-1/2*I*Pi*csgn(I*exp(-x)*(exp(2*x)+1))^3*x+ln(exp(x))*ln(exp(2*x)+1)-ln(exp(x))*ln(1+I*exp(x))-ln(exp(x))*ln(1-I*exp(x))-dilog(1+I*exp(x))-dilog(1-I*exp(x))","C"
205,1,478,33,2.355000," ","int(ln(a*cosh(x)^2),x)","-\frac{i \pi  x \,\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)^{2} {\mathrm e}^{-2 x}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)^{2} a \,{\mathrm e}^{-2 x}\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)^{2} a \,{\mathrm e}^{-2 x}\right)^{2}}{2}-\frac{i \pi  x \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)\right)^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)^{2}\right)}{2}+i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)^{2}\right)^{2}-\frac{i \pi  x \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)^{2}\right)^{3}}{2}-\frac{i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)^{2}\right) \mathrm{csgn}\left(i {\mathrm e}^{-2 x}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)^{2} {\mathrm e}^{-2 x}\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)^{2}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)^{2} {\mathrm e}^{-2 x}\right)^{2}}{2}+\frac{i \pi  x \mathrm{csgn}\left(i {\mathrm e}^{x}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{2 x}\right)}{2}-i \pi  x \,\mathrm{csgn}\left(i {\mathrm e}^{x}\right) \mathrm{csgn}\left(i {\mathrm e}^{2 x}\right)^{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i {\mathrm e}^{-2 x}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)^{2} {\mathrm e}^{-2 x}\right)^{2}}{2}+\frac{i \pi  x \mathrm{csgn}\left(i {\mathrm e}^{2 x}\right)^{3}}{2}-\frac{i \pi  x \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)^{2} {\mathrm e}^{-2 x}\right)^{3}}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)^{2} {\mathrm e}^{-2 x}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)^{2} a \,{\mathrm e}^{-2 x}\right)^{2}}{2}-\frac{i \pi  x \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)^{2} a \,{\mathrm e}^{-2 x}\right)^{3}}{2}+x^{2}+x \ln \left(a \right)-2 x \ln \left({\mathrm e}^{x}\right)-2 \ln \left(-i {\mathrm e}^{x}+1\right) \ln \left({\mathrm e}^{x}\right)-2 \ln \left(i {\mathrm e}^{x}+1\right) \ln \left({\mathrm e}^{x}\right)+2 \ln \left({\mathrm e}^{2 x}+1\right) \ln \left({\mathrm e}^{x}\right)-2 \ln \left(2\right) x -2 \dilog \left(-i {\mathrm e}^{x}+1\right)-2 \dilog \left(i {\mathrm e}^{x}+1\right)"," ",0,"-2*ln(2)*x+x*ln(a)+x^2+2*ln(exp(2*x)+1)*ln(exp(x))-1/2*I*Pi*csgn(I*a)*csgn(I*exp(-2*x)*(exp(2*x)+1)^2)*csgn(I*a*(exp(2*x)+1)^2*exp(-2*x))*x-2*ln(I*exp(x)+1)*ln(exp(x))-2*ln(-I*exp(x)+1)*ln(exp(x))-2*dilog(I*exp(x)+1)-2*dilog(-I*exp(x)+1)+1/2*I*Pi*csgn(I*exp(-2*x)*(exp(2*x)+1)^2)*csgn(I*a*(exp(2*x)+1)^2*exp(-2*x))^2*x+1/2*I*Pi*csgn(I*(exp(2*x)+1)^2)*csgn(I*exp(-2*x)*(exp(2*x)+1)^2)^2*x-I*Pi*x*csgn(I*exp(x))*csgn(I*exp(2*x))^2-2*x*ln(exp(x))-1/2*I*Pi*csgn(I*exp(-2*x)*(exp(2*x)+1)^2)^3*x+1/2*I*Pi*x*csgn(I*exp(x))^2*csgn(I*exp(2*x))+I*Pi*csgn(I*(exp(2*x)+1))*csgn(I*(exp(2*x)+1)^2)^2*x+1/2*I*Pi*x*csgn(I*exp(2*x))^3-1/2*I*Pi*csgn(I*exp(-2*x))*csgn(I*(exp(2*x)+1)^2)*csgn(I*exp(-2*x)*(exp(2*x)+1)^2)*x-1/2*I*Pi*csgn(I*(exp(2*x)+1))^2*csgn(I*(exp(2*x)+1)^2)*x+1/2*I*Pi*csgn(I*exp(-2*x))*csgn(I*exp(-2*x)*(exp(2*x)+1)^2)^2*x+1/2*I*Pi*csgn(I*a)*csgn(I*a*(exp(2*x)+1)^2*exp(-2*x))^2*x-1/2*I*Pi*csgn(I*(exp(2*x)+1)^2)^3*x-1/2*I*Pi*csgn(I*a*(exp(2*x)+1)^2*exp(-2*x))^3*x","C"
206,0,0,38,1.979000," ","int(ln(a*cosh(x)^n),x)","\int \ln \left(a \left(\cosh^{n}\left(x \right)\right)\right)\, dx"," ",0,"int(ln(a*cosh(x)^n),x)","F"
207,1,24,32,0.144000," ","int(ln(tanh(x)),x)","\frac{\ln \left(\tanh \left(x \right)+1\right) \ln \left(\tanh \left(x \right)\right)}{2}+\frac{\dilog \left(\tanh \left(x \right)+1\right)}{2}+\frac{\dilog \left(\tanh \left(x \right)\right)}{2}"," ",0,"1/2*dilog(tanh(x))+1/2*dilog(tanh(x)+1)+1/2*ln(tanh(x))*ln(tanh(x)+1)","A"
208,1,70,34,0.158000," ","int(ln(a*tanh(x)),x)","\frac{\ln \left(a \tanh \left(x \right)\right) \ln \left(\frac{a \tanh \left(x \right)+a}{a}\right)}{2}-\frac{\ln \left(a \tanh \left(x \right)\right) \ln \left(-\frac{a \tanh \left(x \right)-a}{a}\right)}{2}+\frac{\dilog \left(\frac{a \tanh \left(x \right)+a}{a}\right)}{2}-\frac{\dilog \left(-\frac{a \tanh \left(x \right)-a}{a}\right)}{2}"," ",0,"-1/2*ln(a*tanh(x))*ln(-(a*tanh(x)-a)/a)-1/2*dilog(-(a*tanh(x)-a)/a)+1/2*ln(a*tanh(x))*ln((a*tanh(x)+a)/a)+1/2*dilog((a*tanh(x)+a)/a)","B"
209,1,47,34,0.343000," ","int(ln(a*tanh(x)^2),x)","-\frac{\ln \left(a \left(\tanh^{2}\left(x \right)\right)\right) \ln \left(\tanh \left(x \right)-1\right)}{2}+\frac{\ln \left(a \left(\tanh^{2}\left(x \right)\right)\right) \ln \left(\tanh \left(x \right)+1\right)}{2}+\ln \left(\tanh \left(x \right)-1\right) \ln \left(\tanh \left(x \right)\right)+\dilog \left(\tanh \left(x \right)+1\right)+\dilog \left(\tanh \left(x \right)\right)"," ",0,"-1/2*ln(tanh(x)-1)*ln(a*tanh(x)^2)+dilog(tanh(x))+ln(tanh(x)-1)*ln(tanh(x))+1/2*ln(tanh(x)+1)*ln(a*tanh(x)^2)+dilog(tanh(x)+1)","A"
210,1,43,39,0.230000," ","int(ln(a*tanh(x)^n),x)","\frac{n \ln \left(\tanh \left(x \right)+1\right) \ln \left(\tanh \left(x \right)\right)}{2}+\frac{n \dilog \left(\tanh \left(x \right)+1\right)}{2}+\frac{n \dilog \left(\tanh \left(x \right)\right)}{2}+\left(-n \ln \left(\tanh \left(x \right)\right)+\ln \left(a \left(\tanh^{n}\left(x \right)\right)\right)\right) x"," ",0,"(ln(a*tanh(x)^n)-n*ln(tanh(x)))*x+1/2*n*dilog(tanh(x))+1/2*n*dilog(tanh(x)+1)+1/2*n*ln(tanh(x))*ln(tanh(x)+1)","A"
211,1,24,32,0.145000," ","int(ln(coth(x)),x)","\frac{\ln \left(\coth \left(x \right)+1\right) \ln \left(\coth \left(x \right)\right)}{2}+\frac{\dilog \left(\coth \left(x \right)+1\right)}{2}+\frac{\dilog \left(\coth \left(x \right)\right)}{2}"," ",0,"1/2*dilog(coth(x))+1/2*dilog(coth(x)+1)+1/2*ln(coth(x))*ln(coth(x)+1)","A"
212,1,70,34,0.151000," ","int(ln(a*coth(x)),x)","\frac{\ln \left(a \coth \left(x \right)\right) \ln \left(\frac{a \coth \left(x \right)+a}{a}\right)}{2}-\frac{\ln \left(a \coth \left(x \right)\right) \ln \left(-\frac{a \coth \left(x \right)-a}{a}\right)}{2}+\frac{\dilog \left(\frac{a \coth \left(x \right)+a}{a}\right)}{2}-\frac{\dilog \left(-\frac{a \coth \left(x \right)-a}{a}\right)}{2}"," ",0,"-1/2*ln(a*coth(x))*ln(-(a*coth(x)-a)/a)-1/2*dilog(-(a*coth(x)-a)/a)+1/2*ln(a*coth(x))*ln((a*coth(x)+a)/a)+1/2*dilog((a*coth(x)+a)/a)","B"
213,1,47,34,0.273000," ","int(ln(a*coth(x)^2),x)","-\frac{\ln \left(a \left(\coth^{2}\left(x \right)\right)\right) \ln \left(\coth \left(x \right)-1\right)}{2}+\frac{\ln \left(a \left(\coth^{2}\left(x \right)\right)\right) \ln \left(\coth \left(x \right)+1\right)}{2}+\ln \left(\coth \left(x \right)-1\right) \ln \left(\coth \left(x \right)\right)+\dilog \left(\coth \left(x \right)+1\right)+\dilog \left(\coth \left(x \right)\right)"," ",0,"-1/2*ln(coth(x)-1)*ln(a*coth(x)^2)+dilog(coth(x))+ln(coth(x)-1)*ln(coth(x))+1/2*ln(coth(x)+1)*ln(a*coth(x)^2)+dilog(coth(x)+1)","A"
214,1,43,39,0.237000," ","int(ln(a*coth(x)^n),x)","\frac{n \ln \left(\coth \left(x \right)+1\right) \ln \left(\coth \left(x \right)\right)}{2}+\frac{n \dilog \left(\coth \left(x \right)+1\right)}{2}+\frac{n \dilog \left(\coth \left(x \right)\right)}{2}+\left(-n \ln \left(\coth \left(x \right)\right)+\ln \left(a \left(\coth^{n}\left(x \right)\right)\right)\right) x"," ",0,"(ln(a*coth(x)^n)-n*ln(coth(x)))*x+1/2*n*dilog(coth(x))+1/2*n*dilog(coth(x)+1)+1/2*n*ln(coth(x))*ln(coth(x)+1)","A"
215,1,314,32,1.149000," ","int(ln(a*sech(x)),x)","-\frac{i \pi  x \,\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{x}}{{\mathrm e}^{2 x}+1}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{x}}{{\mathrm e}^{2 x}+1}\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{x}}{{\mathrm e}^{2 x}+1}\right)^{2}}{2}-\frac{i \pi  x \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 x}+1}\right) \mathrm{csgn}\left(i {\mathrm e}^{x}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{x}}{{\mathrm e}^{2 x}+1}\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 x}+1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{x}}{{\mathrm e}^{2 x}+1}\right)^{2}}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i {\mathrm e}^{x}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{x}}{{\mathrm e}^{2 x}+1}\right)^{2}}{2}-\frac{i \pi  x \mathrm{csgn}\left(\frac{i {\mathrm e}^{x}}{{\mathrm e}^{2 x}+1}\right)^{3}}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{x}}{{\mathrm e}^{2 x}+1}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{x}}{{\mathrm e}^{2 x}+1}\right)^{2}}{2}-\frac{i \pi  x \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{x}}{{\mathrm e}^{2 x}+1}\right)^{3}}{2}-\frac{x^{2}}{2}+x \ln \left(a \right)+x \ln \left({\mathrm e}^{x}\right)+\ln \left(-i {\mathrm e}^{x}+1\right) \ln \left({\mathrm e}^{x}\right)+\ln \left(i {\mathrm e}^{x}+1\right) \ln \left({\mathrm e}^{x}\right)-\ln \left({\mathrm e}^{2 x}+1\right) \ln \left({\mathrm e}^{x}\right)+\ln \left(2\right) x +\dilog \left(-i {\mathrm e}^{x}+1\right)+\dilog \left(i {\mathrm e}^{x}+1\right)"," ",0,"x*ln(exp(x))+1/2*I*Pi*csgn(I/(exp(2*x)+1))*csgn(I*exp(x)/(exp(2*x)+1))^2*x-1/2*I*Pi*csgn(I*a)*csgn(I*exp(x)/(exp(2*x)+1))*csgn(I*a/(exp(2*x)+1)*exp(x))*x+1/2*I*Pi*csgn(I*exp(x))*csgn(I*exp(x)/(exp(2*x)+1))^2*x-1/2*I*Pi*csgn(I*exp(x))*csgn(I/(exp(2*x)+1))*csgn(I*exp(x)/(exp(2*x)+1))*x-1/2*I*Pi*csgn(I*a/(exp(2*x)+1)*exp(x))^3*x+1/2*I*Pi*csgn(I*a)*csgn(I*a/(exp(2*x)+1)*exp(x))^2*x+ln(2)*x+x*ln(a)-1/2*x^2+1/2*I*Pi*csgn(I*exp(x)/(exp(2*x)+1))*csgn(I*a/(exp(2*x)+1)*exp(x))^2*x-1/2*I*Pi*csgn(I*exp(x)/(exp(2*x)+1))^3*x-ln(exp(2*x)+1)*ln(exp(x))+ln(I*exp(x)+1)*ln(exp(x))+ln(-I*exp(x)+1)*ln(exp(x))+dilog(I*exp(x)+1)+dilog(-I*exp(x)+1)","C"
216,1,480,33,1.412000," ","int(ln(a*sech(x)^2),x)","-\frac{i \pi  x \,\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}+1\right)^{2}}\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}+1\right)^{2}}\right)^{2}}{2}-\frac{i \pi  x \,\mathrm{csgn}\left(\frac{i}{\left({\mathrm e}^{2 x}+1\right)^{2}}\right) \mathrm{csgn}\left(i {\mathrm e}^{2 x}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}+1\right)^{2}}\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(\frac{i}{\left({\mathrm e}^{2 x}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}+1\right)^{2}}\right)^{2}}{2}+\frac{i \pi  x \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)\right)^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)^{2}\right)}{2}-i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)^{2}\right)^{2}+\frac{i \pi  x \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1\right)^{2}\right)^{3}}{2}-\frac{i \pi  x \mathrm{csgn}\left(i {\mathrm e}^{x}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{2 x}\right)}{2}+i \pi  x \,\mathrm{csgn}\left(i {\mathrm e}^{x}\right) \mathrm{csgn}\left(i {\mathrm e}^{2 x}\right)^{2}-\frac{i \pi  x \mathrm{csgn}\left(i {\mathrm e}^{2 x}\right)^{3}}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i {\mathrm e}^{2 x}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}+1\right)^{2}}\right)^{2}}{2}-\frac{i \pi  x \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}+1\right)^{2}}\right)^{3}}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}+1\right)^{2}}\right)^{2}}{2}-\frac{i \pi  x \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}+1\right)^{2}}\right)^{3}}{2}-x^{2}+x \ln \left(a \right)+2 x \ln \left({\mathrm e}^{x}\right)+2 \ln \left(-i {\mathrm e}^{x}+1\right) \ln \left({\mathrm e}^{x}\right)+2 \ln \left(i {\mathrm e}^{x}+1\right) \ln \left({\mathrm e}^{x}\right)-2 \ln \left({\mathrm e}^{2 x}+1\right) \ln \left({\mathrm e}^{x}\right)+2 \ln \left(2\right) x +2 \dilog \left(-i {\mathrm e}^{x}+1\right)+2 \dilog \left(i {\mathrm e}^{x}+1\right)"," ",0,"2*ln(2)*x+x*ln(a)-x^2-2*ln(exp(2*x)+1)*ln(exp(x))+2*ln(I*exp(x)+1)*ln(exp(x))+2*ln(-I*exp(x)+1)*ln(exp(x))+2*dilog(I*exp(x)+1)+2*dilog(-I*exp(x)+1)+1/2*I*Pi*csgn(I*(exp(2*x)+1)^2)^3*x-1/2*I*Pi*csgn(I*exp(2*x)/(exp(2*x)+1)^2)^3*x+I*Pi*csgn(I*exp(x))*csgn(I*exp(2*x))^2*x+1/2*I*Pi*csgn(I*a)*csgn(I*a/(exp(2*x)+1)^2*exp(2*x))^2*x+1/2*I*Pi*csgn(I*exp(2*x)/(exp(2*x)+1)^2)*csgn(I*a/(exp(2*x)+1)^2*exp(2*x))^2*x-1/2*I*Pi*csgn(I*exp(2*x))^3*x+1/2*I*Pi*csgn(I*(exp(2*x)+1))^2*csgn(I*(exp(2*x)+1)^2)*x-1/2*I*Pi*csgn(I*exp(x))^2*csgn(I*exp(2*x))*x-I*Pi*csgn(I*(exp(2*x)+1))*csgn(I*(exp(2*x)+1)^2)^2*x-1/2*I*Pi*csgn(I*a/(exp(2*x)+1)^2*exp(2*x))^3*x+2*x*ln(exp(x))-1/2*I*Pi*csgn(I*a)*csgn(I*exp(2*x)/(exp(2*x)+1)^2)*csgn(I*a/(exp(2*x)+1)^2*exp(2*x))*x+1/2*I*Pi*csgn(I*exp(2*x))*csgn(I*exp(2*x)/(exp(2*x)+1)^2)^2*x-1/2*I*Pi*csgn(I*exp(2*x))*csgn(I/(exp(2*x)+1)^2)*csgn(I*exp(2*x)/(exp(2*x)+1)^2)*x+1/2*I*Pi*csgn(I/(exp(2*x)+1)^2)*csgn(I*exp(2*x)/(exp(2*x)+1)^2)^2*x","C"
217,0,0,37,1.857000," ","int(ln(a*sech(x)^n),x)","\int \ln \left(a \mathrm{sech}\left(x \right)^{n}\right)\, dx"," ",0,"int(ln(a*sech(x)^n),x)","F"
218,1,293,32,0.949000," ","int(ln(a*csch(x)),x)","-\frac{i \pi  x \,\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{x}}{{\mathrm e}^{2 x}-1}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{x}}{{\mathrm e}^{2 x}-1}\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{x}}{{\mathrm e}^{2 x}-1}\right)^{2}}{2}-\frac{i \pi  x \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 x}-1}\right) \mathrm{csgn}\left(i {\mathrm e}^{x}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{x}}{{\mathrm e}^{2 x}-1}\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 x}-1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{x}}{{\mathrm e}^{2 x}-1}\right)^{2}}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i {\mathrm e}^{x}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{x}}{{\mathrm e}^{2 x}-1}\right)^{2}}{2}-\frac{i \pi  x \mathrm{csgn}\left(\frac{i {\mathrm e}^{x}}{{\mathrm e}^{2 x}-1}\right)^{3}}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{x}}{{\mathrm e}^{2 x}-1}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{x}}{{\mathrm e}^{2 x}-1}\right)^{2}}{2}-\frac{i \pi  x \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{x}}{{\mathrm e}^{2 x}-1}\right)^{3}}{2}-\frac{x^{2}}{2}+x \ln \left(a \right)+x \ln \left({\mathrm e}^{x}\right)-\ln \left({\mathrm e}^{2 x}-1\right) \ln \left({\mathrm e}^{x}\right)+\ln \left({\mathrm e}^{x}+1\right) \ln \left({\mathrm e}^{x}\right)+\ln \left(2\right) x +\dilog \left({\mathrm e}^{x}+1\right)-\dilog \left({\mathrm e}^{x}\right)"," ",0,"x*ln(exp(x))+1/2*I*Pi*csgn(I*exp(x))*csgn(I*exp(x)/(exp(2*x)-1))^2*x+1/2*I*Pi*csgn(I*exp(x)/(exp(2*x)-1))*csgn(I*a/(exp(2*x)-1)*exp(x))^2*x-1/2*I*Pi*csgn(I*exp(x))*csgn(I/(exp(2*x)-1))*csgn(I*exp(x)/(exp(2*x)-1))*x-1/2*I*Pi*csgn(I*a)*csgn(I*exp(x)/(exp(2*x)-1))*csgn(I*a/(exp(2*x)-1)*exp(x))*x-1/2*I*Pi*csgn(I*exp(x)/(exp(2*x)-1))^3*x+1/2*I*Pi*csgn(I*a)*csgn(I*a/(exp(2*x)-1)*exp(x))^2*x+ln(2)*x+x*ln(a)-1/2*x^2-1/2*I*Pi*csgn(I*a/(exp(2*x)-1)*exp(x))^3*x+1/2*I*Pi*csgn(I/(exp(2*x)-1))*csgn(I*exp(x)/(exp(2*x)-1))^2*x-ln(exp(2*x)-1)*ln(exp(x))-dilog(exp(x))+dilog(exp(x)+1)+ln(exp(x)+1)*ln(exp(x))","C"
219,1,456,33,1.344000," ","int(ln(a*csch(x)^2),x)","-\frac{i \pi  x \,\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}-1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}-1\right)^{2}}\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i a \right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}-1\right)^{2}}\right)^{2}}{2}-\frac{i \pi  x \,\mathrm{csgn}\left(\frac{i}{\left({\mathrm e}^{2 x}-1\right)^{2}}\right) \mathrm{csgn}\left(i {\mathrm e}^{2 x}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}-1\right)^{2}}\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(\frac{i}{\left({\mathrm e}^{2 x}-1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}-1\right)^{2}}\right)^{2}}{2}+\frac{i \pi  x \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)\right)^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)^{2}\right)}{2}-i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)^{2}\right)^{2}+\frac{i \pi  x \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}-1\right)^{2}\right)^{3}}{2}-\frac{i \pi  x \mathrm{csgn}\left(i {\mathrm e}^{x}\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{2 x}\right)}{2}+i \pi  x \,\mathrm{csgn}\left(i {\mathrm e}^{x}\right) \mathrm{csgn}\left(i {\mathrm e}^{2 x}\right)^{2}-\frac{i \pi  x \mathrm{csgn}\left(i {\mathrm e}^{2 x}\right)^{3}}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i {\mathrm e}^{2 x}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}-1\right)^{2}}\right)^{2}}{2}-\frac{i \pi  x \mathrm{csgn}\left(\frac{i {\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}-1\right)^{2}}\right)^{3}}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}-1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}-1\right)^{2}}\right)^{2}}{2}-\frac{i \pi  x \mathrm{csgn}\left(\frac{i a \,{\mathrm e}^{2 x}}{\left({\mathrm e}^{2 x}-1\right)^{2}}\right)^{3}}{2}-x^{2}+x \ln \left(a \right)+2 x \ln \left({\mathrm e}^{x}\right)-2 \ln \left({\mathrm e}^{2 x}-1\right) \ln \left({\mathrm e}^{x}\right)+2 \ln \left({\mathrm e}^{x}+1\right) \ln \left({\mathrm e}^{x}\right)+2 \ln \left(2\right) x +2 \dilog \left({\mathrm e}^{x}+1\right)-2 \dilog \left({\mathrm e}^{x}\right)"," ",0,"2*ln(2)*x+x*ln(a)-x^2-2*dilog(exp(x))+2*dilog(exp(x)+1)-I*Pi*csgn(I*(exp(2*x)-1))*csgn(I*(exp(2*x)-1)^2)^2*x+1/2*I*Pi*csgn(I*exp(2*x)/(exp(2*x)-1)^2)*csgn(I*a/(exp(2*x)-1)^2*exp(2*x))^2*x-1/2*I*Pi*csgn(I*exp(x))^2*csgn(I*exp(2*x))*x-1/2*I*Pi*csgn(I*exp(2*x))*csgn(I/(exp(2*x)-1)^2)*csgn(I*exp(2*x)/(exp(2*x)-1)^2)*x+1/2*I*Pi*csgn(I*(exp(2*x)-1)^2)^3*x-1/2*I*Pi*csgn(I*a/(exp(2*x)-1)^2*exp(2*x))^3*x-1/2*I*Pi*csgn(I*a)*csgn(I*exp(2*x)/(exp(2*x)-1)^2)*csgn(I*a/(exp(2*x)-1)^2*exp(2*x))*x+2*ln(exp(x)+1)*ln(exp(x))+2*x*ln(exp(x))-2*ln(exp(2*x)-1)*ln(exp(x))+1/2*I*Pi*csgn(I*exp(2*x))*csgn(I*exp(2*x)/(exp(2*x)-1)^2)^2*x-1/2*I*Pi*csgn(I*exp(2*x)/(exp(2*x)-1)^2)^3*x+1/2*I*Pi*csgn(I/(exp(2*x)-1)^2)*csgn(I*exp(2*x)/(exp(2*x)-1)^2)^2*x+1/2*I*Pi*csgn(I*(exp(2*x)-1))^2*csgn(I*(exp(2*x)-1)^2)*x+1/2*I*Pi*csgn(I*a)*csgn(I*a/(exp(2*x)-1)^2*exp(2*x))^2*x+I*Pi*csgn(I*exp(x))*csgn(I*exp(2*x))^2*x-1/2*I*Pi*csgn(I*exp(2*x))^3*x","C"
220,0,0,37,2.080000," ","int(ln(a*csch(x)^n),x)","\int \ln \left(a \mathrm{csch}\left(x \right)^{n}\right)\, dx"," ",0,"int(ln(a*csch(x)^n),x)","F"
221,1,32,42,0.889000," ","int(cosh(b*x+a)*ln(cosh(1/2*b*x+1/2*a)*sinh(1/2*b*x+1/2*a)),x)","\frac{\ln \left(\frac{\sinh \left(b x +a \right)}{2}\right) \sinh \left(b x +a \right)}{b}-\frac{\sinh \left(b x +a \right)}{b}"," ",0,"ln(1/2*sinh(b*x+a))/b*sinh(b*x+a)-sinh(b*x+a)/b","A"
222,1,14,13,0.288000," ","int(ln(cosh(x)^2)*sinh(x),x)","\cosh \left(x \right) \ln \left(\cosh^{2}\left(x \right)\right)-2 \cosh \left(x \right)"," ",0,"-2*cosh(x)+cosh(x)*ln(cosh(x)^2)","A"
223,1,14,13,0.072000," ","int(ln(x)/x^(1/2),x)","2 \sqrt{x}\, \ln \left(x \right)-4 \sqrt{x}"," ",0,"-4*x^(1/2)+2*ln(x)*x^(1/2)","A"
224,1,25,23,0.063000," ","int(x*ln(-3*x^2+2),x)","-\frac{x^{2}}{2}-\frac{\left(-3 x^{2}+2\right) \ln \left(-3 x^{2}+2\right)}{6}+\frac{1}{3}"," ",0,"-1/6*(-3*x^2+2)*ln(-3*x^2+2)-1/2*x^2+1/3","A"
225,1,4,3,0.064000," ","int(1/x/(1-ln(x)^2)^(1/2),x)","\arcsin \left(\ln \left(x \right)\right)"," ",0,"arcsin(ln(x))","A"
226,1,23,22,0.063000," ","int(16*x^3*ln(x)^2,x)","4 x^{4} \ln \left(x \right)^{2}-2 x^{4} \ln \left(x \right)+\frac{x^{4}}{2}"," ",0,"1/2*x^4-2*x^4*ln(x)+4*x^4*ln(x)^2","A"
227,1,32,20,0.066000," ","int(1/2*ln(b*x+a),x)","\frac{x \ln \left(b x +a \right)}{2}+\frac{a \ln \left(b x +a \right)}{2 b}-\frac{x}{2}-\frac{a}{2 b}"," ",0,"1/2*x*ln(b*x+a)+1/2*a/b*ln(b*x+a)-1/2*x-1/2*a/b","A"
228,1,31,24,0.065000," ","int(1/2*x*ln(x+2),x)","-\frac{x^{2}}{8}+\frac{x}{2}-\left(x +2\right) \ln \left(x +2\right)+\frac{\left(x +2\right)^{2} \ln \left(x +2\right)}{4}+\frac{3}{2}"," ",0,"-(x+2)*ln(x+2)+1/2*x+3/2+1/4*(x+2)^2*ln(x+2)-1/8*x^2","A"
229,1,39,28,0.068000," ","int(1/3*x*ln(1+3*x),x)","-\frac{x^{2}}{12}+\frac{x}{18}+\frac{\left(3 x +1\right)^{2} \ln \left(3 x +1\right)}{54}-\frac{\left(3 x +1\right) \ln \left(3 x +1\right)}{27}+\frac{1}{36}"," ",0,"1/54*(1+3*x)^2*ln(1+3*x)-1/12*x^2+1/18*x+1/36-1/27*(1+3*x)*ln(1+3*x)","A"
230,1,26,25,0.065000," ","int(x*ln(x^3+x),x)","\frac{x^{2} \ln \left(x^{3}+x \right)}{2}-\frac{3 x^{2}}{4}+\frac{\ln \left(x^{2}+1\right)}{2}"," ",0,"-3/4*x^2+1/2*ln(x^2+1)+1/2*x^2*ln(x^3+x)","A"
231,1,23,22,0.066000," ","int(ln(x+(x^2+1)^(1/2)),x)","x \ln \left(x +\sqrt{x^{2}+1}\right)-\sqrt{x^{2}+1}"," ",0,"x*ln(x+(x^2+1)^(1/2))-(x^2+1)^(1/2)","A"
232,1,23,22,0.073000," ","int(ln(x+(x^2-1)^(1/2)),x)","x \ln \left(x +\sqrt{x^{2}-1}\right)-\sqrt{x^{2}-1}"," ",0,"x*ln(x+(x^2-1)^(1/2))-(x^2-1)^(1/2)","A"
233,1,23,22,0.067000," ","int(ln(x-(x^2-1)^(1/2)),x)","x \ln \left(x -\sqrt{x^{2}-1}\right)+\sqrt{x^{2}-1}"," ",0,"x*ln(x-(x^2-1)^(1/2))+(x^2-1)^(1/2)","A"
234,1,52,29,0.071000," ","int(ln(x^(1/2)+(x+1)^(1/2)),x)","x \ln \left(\sqrt{x}+\sqrt{x +1}\right)-\frac{\sqrt{x +1}\, \sqrt{x}}{2}+\frac{\sqrt{\left(x +1\right) x}\, \ln \left(x +\frac{1}{2}+\sqrt{x^{2}+x}\right)}{4 \sqrt{x +1}\, \sqrt{x}}"," ",0,"x*ln(x^(1/2)+(x+1)^(1/2))-1/2*(x+1)^(1/2)*x^(1/2)+1/4*(x*(x+1))^(1/2)/x^(1/2)/(x+1)^(1/2)*ln(x+1/2+(x^2+x)^(1/2))","A"
235,1,14,13,0.066000," ","int(x^(1/3)*ln(x),x)","\frac{3 x^{\frac{4}{3}} \ln \left(x \right)}{4}-\frac{9 x^{\frac{4}{3}}}{16}"," ",0,"-9/16*x^(4/3)+3/4*x^(4/3)*ln(x)","A"
236,1,13,13,0.065000," ","int(2^ln(x),x)","\frac{x 2^{\ln \left(x \right)}}{1+\ln \left(2\right)}"," ",0,"x/(1+ln(2))*2^ln(x)","A"
237,1,7,6,0.065000," ","int((1-ln(x))/x^2,x)","\frac{\ln \left(x \right)}{x}"," ",0,"ln(x)/x","A"
238,1,34,26,0.072000," ","int(ln(x+1+(x+1)^(1/2)),x)","-x -\ln \left(1+\sqrt{x +1}\right)+\left(x +1\right) \ln \left(x +1+\sqrt{x +1}\right)-1+\sqrt{x +1}"," ",0,"(x+1)*ln(x+1+(x+1)^(1/2))-x-1+(x+1)^(1/2)-ln(1+(x+1)^(1/2))","A"
239,1,17,16,0.070000," ","int(ln(x^3+x),x)","x \ln \left(x^{3}+x \right)-3 x +2 \arctan \left(x \right)"," ",0,"-3*x+2*arctan(x)+x*ln(x^3+x)","A"
240,1,22,18,0.067000," ","int(2^ln(-8+7*x),x)","\frac{\left(7 x -8\right) 2^{\ln \left(7 x -8\right)}}{7 \ln \left(2\right)+7}"," ",0,"1/7*(-8+7*x)/(1+ln(2))*2^ln(-8+7*x)","A"
241,1,44,30,0.166000," ","int(ln((-11+5*x)/(5+76*x)),x)","\frac{861 \ln \left(-\frac{861}{76 x +5}\right)}{380}+\frac{\left(\frac{5}{76}-\frac{861}{76 \left(76 x +5\right)}\right) \left(76 x +5\right) \ln \left(\frac{5}{76}-\frac{861}{76 \left(76 x +5\right)}\right)}{5}"," ",0,"861/380*ln(-861/(5+76*x))+1/5*ln(5/76-861/76/(5+76*x))*(5/76-861/76/(5+76*x))*(5+76*x)","A"
242,1,14,12,0.073000," ","int(ln(1/(13+x)),x)","x +\left(x +13\right) \ln \left(\frac{1}{x +13}\right)+13"," ",0,"(13+x)*ln(1/(13+x))+13+x","A"
243,1,39,28,0.085000," ","int(x*ln((x+1)/x^2),x)","\frac{x^{2} \ln \left(\frac{\frac{1}{x}+1}{x}\right)}{2}+\frac{x^{2}}{4}+\frac{x}{2}+\frac{\ln \left(\frac{1}{x}\right)}{2}-\frac{\ln \left(\frac{1}{x}+1\right)}{2}"," ",0,"1/2*x^2*ln(1/x*(1+1/x))-1/2*ln(1+1/x)+1/4*x^2+1/2*x+1/2*ln(1/x)","A"
244,1,53,42,0.084000," ","int(x^3*ln((7+5*x)/x^2),x)","\frac{x^{4} \ln \left(\frac{\frac{7}{x}+5}{x}\right)}{4}+\frac{x^{4}}{16}+\frac{7 x^{3}}{60}-\frac{49 x^{2}}{200}+\frac{343 x}{500}+\frac{2401 \ln \left(\frac{1}{x}\right)}{2500}-\frac{2401 \ln \left(\frac{7}{x}+5\right)}{2500}"," ",0,"1/4*x^4*ln((7/x+5)/x)-2401/2500*ln(7/x+5)+1/16*x^4+7/60*x^3-49/200*x^2+343/500*x+2401/2500*ln(1/x)","A"
245,1,55,31,0.066000," ","int((b*x+a)*ln(b*x+a),x)","\frac{b \,x^{2} \ln \left(b x +a \right)}{2}+a x \ln \left(b x +a \right)-\frac{b \,x^{2}}{4}+\frac{a^{2} \ln \left(b x +a \right)}{2 b}-\frac{a x}{2}-\frac{a^{2}}{4 b}"," ",0,"1/2*b*ln(b*x+a)*x^2+ln(b*x+a)*x*a+1/2/b*ln(b*x+a)*a^2-1/4*b*x^2-1/2*a*x-1/4/b*a^2","A"
246,1,82,31,0.069000," ","int((b*x+a)^2*ln(b*x+a),x)","\frac{b^{2} x^{3} \ln \left(b x +a \right)}{3}+a b \,x^{2} \ln \left(b x +a \right)-\frac{b^{2} x^{3}}{9}+a^{2} x \ln \left(b x +a \right)-\frac{a b \,x^{2}}{3}+\frac{a^{3} \ln \left(b x +a \right)}{3 b}-\frac{a^{2} x}{3}-\frac{a^{3}}{9 b}"," ",0,"1/3*b^2*ln(b*x+a)*x^3+b*ln(b*x+a)*x^2*a+ln(b*x+a)*x*a^2+1/3/b*ln(b*x+a)*a^3-1/9*b^2*x^3-1/3*a*b*x^2-1/3*a^2*x-1/9/b*a^3","B"
247,1,14,13,0.063000," ","int(ln(b*x+a)/(b*x+a),x)","\frac{\ln \left(b x +a \right)^{2}}{2 b}"," ",0,"1/2*ln(b*x+a)^2/b","A"
248,1,32,31,0.079000," ","int(ln(b*x+a)/(b*x+a)^2,x)","-\frac{\ln \left(b x +a \right)}{\left(b x +a \right) b}-\frac{1}{\left(b x +a \right) b}"," ",0,"-1/b/(b*x+a)-ln(b*x+a)/b/(b*x+a)","A"
249,1,96,44,0.073000," ","int((b*x+a)^n*ln(b*x+a),x)","\frac{x \,{\mathrm e}^{n \ln \left(b x +a \right)} \ln \left(b x +a \right)}{n +1}+\frac{a \,{\mathrm e}^{n \ln \left(b x +a \right)} \ln \left(b x +a \right)}{\left(n +1\right) b}-\frac{x \,{\mathrm e}^{n \ln \left(b x +a \right)}}{n^{2}+2 n +1}-\frac{a \,{\mathrm e}^{n \ln \left(b x +a \right)}}{\left(n^{2}+2 n +1\right) b}"," ",0,"1/(n+1)*x*ln(b*x+a)*exp(n*ln(b*x+a))+a/b/(n+1)*ln(b*x+a)*exp(n*ln(b*x+a))-1/(n^2+2*n+1)*x*exp(n*ln(b*x+a))-a/b/(n^2+2*n+1)*exp(n*ln(b*x+a))","B"
250,1,19,18,0.067000," ","int(1/(a*x+b*x*ln(c*x^n)),x)","\frac{\ln \left(b \ln \left(c \,x^{n}\right)+a \right)}{b n}"," ",0,"1/b/n*ln(b*ln(c*x^n)+a)","A"
251,1,24,24,0.071000," ","int(1/(a*x+b*x*ln(c*x^n)^2),x)","\frac{\arctan \left(\frac{b \ln \left(c \,x^{n}\right)}{\sqrt{a b}}\right)}{\sqrt{a b}\, n}"," ",0,"1/n/(a*b)^(1/2)*arctan(b*ln(c*x^n)/(a*b)^(1/2))","A"
252,1,120,107,0.073000," ","int(1/(a*x+b*x*ln(c*x^n)^3),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \ln \left(c \,x^{n}\right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b n}+\frac{\ln \left(\ln \left(c \,x^{n}\right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b n}-\frac{\ln \left(\ln \left(c \,x^{n}\right)^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} \ln \left(c \,x^{n}\right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b n}"," ",0,"1/3/n/b/(a/b)^(2/3)*ln(ln(c*x^n)+(a/b)^(1/3))-1/6/n/b/(a/b)^(2/3)*ln(ln(c*x^n)^2-(a/b)^(1/3)*ln(c*x^n)+(a/b)^(2/3))+1/3/n/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*ln(c*x^n)-1))","A"
253,1,168,163,0.069000," ","int(1/(a*x+b*x*ln(c*x^n)^4),x)","-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \ln \left(c \,x^{n}\right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 a n}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \ln \left(c \,x^{n}\right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 a n}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{\ln \left(c \,x^{n}\right)^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(c \,x^{n}\right)+\sqrt{\frac{a}{b}}}{\ln \left(c \,x^{n}\right)^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(c \,x^{n}\right)+\sqrt{\frac{a}{b}}}\right)}{8 a n}"," ",0,"1/8/n*(a/b)^(1/4)/a*2^(1/2)*ln((ln(c*x^n)^2+(a/b)^(1/4)*ln(c*x^n)*2^(1/2)+(a/b)^(1/2))/(ln(c*x^n)^2-(a/b)^(1/4)*ln(c*x^n)*2^(1/2)+(a/b)^(1/2)))+1/4/n*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*ln(c*x^n)+1)-1/4/n*(a/b)^(1/4)/a*2^(1/2)*arctan(-2^(1/2)/(a/b)^(1/4)*ln(c*x^n)+1)","A"
254,1,35,27,0.070000," ","int(1/(a*x+b*x/ln(c*x^n)),x)","\frac{\ln \left(c \,x^{n}\right)}{a n}-\frac{b \ln \left(a \ln \left(c \,x^{n}\right)+b \right)}{a^{2} n}"," ",0,"1/n*ln(c*x^n)/a-b*ln(b+a*ln(c*x^n))/a^2/n","A"
255,1,43,32,0.071000," ","int(1/(a*x+b*x/ln(c*x^n)^2),x)","-\frac{b \arctan \left(\frac{a \ln \left(c \,x^{n}\right)}{\sqrt{a b}}\right)}{\sqrt{a b}\, a n}+\frac{\ln \left(c \,x^{n}\right)}{a n}"," ",0,"1/a/n*ln(c*x^n)-1/n/a*b/(a*b)^(1/2)*arctan(a*ln(c*x^n)/(a*b)^(1/2))","A"
256,1,136,113,0.070000," ","int(1/(a*x+b*x/ln(c*x^n)^3),x)","\frac{\ln \left(c \,x^{n}\right)}{a n}-\frac{\sqrt{3}\, b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \ln \left(c \,x^{n}\right)}{\left(\frac{b}{a}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{b}{a}\right)^{\frac{2}{3}} a^{2} n}-\frac{b \ln \left(\ln \left(c \,x^{n}\right)+\left(\frac{b}{a}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{b}{a}\right)^{\frac{2}{3}} a^{2} n}+\frac{b \ln \left(\ln \left(c \,x^{n}\right)^{2}-\left(\frac{b}{a}\right)^{\frac{1}{3}} \ln \left(c \,x^{n}\right)+\left(\frac{b}{a}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{b}{a}\right)^{\frac{2}{3}} a^{2} n}"," ",0,"1/a/n*ln(c*x^n)-1/3/n/a^2*b/(1/a*b)^(2/3)*ln(ln(c*x^n)+(1/a*b)^(1/3))+1/6/n/a^2*b/(1/a*b)^(2/3)*ln(ln(c*x^n)^2-(1/a*b)^(1/3)*ln(c*x^n)+(1/a*b)^(2/3))-1/3/n/a^2*b/(1/a*b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/a*b)^(1/3)*ln(c*x^n)-1))","A"
257,1,181,168,0.108000," ","int(1/(a*x+b*x/ln(c*x^n)^4),x)","\frac{\left(\frac{b}{a}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(-\frac{\sqrt{2}\, \ln \left(c \,x^{n}\right)}{\left(\frac{b}{a}\right)^{\frac{1}{4}}}+1\right)}{4 a n}-\frac{\left(\frac{b}{a}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \ln \left(c \,x^{n}\right)}{\left(\frac{b}{a}\right)^{\frac{1}{4}}}+1\right)}{4 a n}+\frac{\ln \left(c \,x^{n}\right)}{a n}-\frac{\left(\frac{b}{a}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{\ln \left(c \,x^{n}\right)^{2}+\left(\frac{b}{a}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(c \,x^{n}\right)+\sqrt{\frac{b}{a}}}{\ln \left(c \,x^{n}\right)^{2}-\left(\frac{b}{a}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(c \,x^{n}\right)+\sqrt{\frac{b}{a}}}\right)}{8 a n}"," ",0,"1/a/n*ln(c*x^n)-1/8/n/a*(1/a*b)^(1/4)*2^(1/2)*ln((ln(c*x^n)^2+(1/a*b)^(1/4)*ln(c*x^n)*2^(1/2)+(1/a*b)^(1/2))/(ln(c*x^n)^2-(1/a*b)^(1/4)*ln(c*x^n)*2^(1/2)+(1/a*b)^(1/2)))-1/4/n/a*(1/a*b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/a*b)^(1/4)*ln(c*x^n)+1)+1/4/n/a*(1/a*b)^(1/4)*2^(1/2)*arctan(-2^(1/2)/(1/a*b)^(1/4)*ln(c*x^n)+1)","A"
258,1,20,19,0.071000," ","int(1/(x+x*ln(7*x)+x*ln(7*x)^2),x)","\frac{2 \sqrt{3}\, \arctan \left(\frac{\left(2 \ln \left(7 x \right)+1\right) \sqrt{3}}{3}\right)}{3}"," ",0,"2/3*arctan(1/3*(1+2*ln(7*x))*3^(1/2))*3^(1/2)","A"
259,1,38,37,0.060000," ","int((-1+ln(3*x))/x/(1-ln(3*x)+ln(3*x)^2),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 \ln \left(3 x \right)-1\right) \sqrt{3}}{3}\right)}{3}+\frac{\ln \left(\ln \left(3 x \right)^{2}-\ln \left(3 x \right)+1\right)}{2}"," ",0,"1/2*ln(1-ln(3*x)+ln(3*x)^2)-1/3*3^(1/2)*arctan(1/3*(-1+2*ln(3*x))*3^(1/2))","A"
260,1,38,37,0.069000," ","int((-1+ln(3*x)^2)/(x+x*ln(3*x)^3),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 \ln \left(3 x \right)-1\right) \sqrt{3}}{3}\right)}{3}+\frac{\ln \left(\ln \left(3 x \right)^{2}-\ln \left(3 x \right)+1\right)}{2}"," ",0,"-1/3*3^(1/2)*arctan(1/3*(2*ln(3*x)-1)*3^(1/2))+1/2*ln(ln(3*x)^2-ln(3*x)+1)","A"
261,1,40,37,0.072000," ","int((-1+ln(3*x)^2)/(x+x*ln(3*x)+x*ln(3*x)^2),x)","-\sqrt{3}\, \arctan \left(\frac{\left(2 \ln \left(3 x \right)+1\right) \sqrt{3}}{3}\right)+\ln \left(3 x \right)-\frac{\ln \left(\ln \left(3 x \right)^{2}+\ln \left(3 x \right)+1\right)}{2}"," ",0,"ln(3*x)-1/2*ln(1+ln(3*x)+ln(3*x)^2)-arctan(1/3*(1+2*ln(3*x))*3^(1/2))*3^(1/2)","A"
262,1,27,26,0.070000," ","int(ln(1/x)^2/x^5,x)","-\frac{\ln \left(\frac{1}{x}\right)^{2}}{4 x^{4}}+\frac{\ln \left(\frac{1}{x}\right)}{8 x^{4}}-\frac{1}{32 x^{4}}"," ",0,"-1/32/x^4+1/8*ln(1/x)/x^4-1/4*ln(1/x)^2/x^4","A"
263,0,0,32,0.113000," ","int(1/(-ln(a*x^2))^(1/2),x)","\int \frac{1}{\sqrt{-\ln \left(a \,x^{2}\right)}}\, dx"," ",0,"int(1/(-ln(a*x^2))^(1/2),x)","F"
264,0,0,32,0.111000," ","int(1/(-ln(a/x^2))^(1/2),x)","\int \frac{1}{\sqrt{-\ln \left(\frac{a}{x^{2}}\right)}}\, dx"," ",0,"int(1/(-ln(a/x^2))^(1/2),x)","F"
265,0,0,35,1.320000," ","int(1/(-ln(a*x^n))^(1/2),x)","\int \frac{1}{\sqrt{-\ln \left(a \,x^{n}\right)}}\, dx"," ",0,"int(1/(-ln(a*x^n))^(1/2),x)","F"
266,1,102,91,0.071000," ","int(ln(1-x+x^(1/2))/x,x)","-\ln \left(x \right) \ln \left(\frac{2 \sqrt{x}-1+\sqrt{5}}{\sqrt{5}-1}\right)-\ln \left(x \right) \ln \left(\frac{-2 \sqrt{x}+1+\sqrt{5}}{\sqrt{5}+1}\right)+\ln \left(x \right) \ln \left(-x +\sqrt{x}+1\right)-2 \dilog \left(\frac{2 \sqrt{x}-1+\sqrt{5}}{\sqrt{5}-1}\right)-2 \dilog \left(\frac{-2 \sqrt{x}+1+\sqrt{5}}{\sqrt{5}+1}\right)"," ",0,"ln(x)*ln(1-x+x^(1/2))-ln(x)*ln((1+5^(1/2)-2*x^(1/2))/(5^(1/2)+1))-ln(x)*ln((-1+5^(1/2)+2*x^(1/2))/(5^(1/2)-1))-2*dilog((1+5^(1/2)-2*x^(1/2))/(5^(1/2)+1))-2*dilog((-1+5^(1/2)+2*x^(1/2))/(5^(1/2)-1))","A"
267,1,114,81,0.077000," ","int(x*ln(d*x+c)/(b*x+a),x)","-\frac{a \ln \left(\frac{a d -b c +\left(d x +c \right) b}{a d -b c}\right) \ln \left(d x +c \right)}{b^{2}}+\frac{x \ln \left(d x +c \right)}{b}-\frac{a \dilog \left(\frac{a d -b c +\left(d x +c \right) b}{a d -b c}\right)}{b^{2}}+\frac{c \ln \left(d x +c \right)}{b d}-\frac{x}{b}-\frac{c}{b d}"," ",0,"1/b*ln(d*x+c)*x+1/d/b*ln(d*x+c)*c-1/b*x-1/d/b*c-a/b^2*dilog((b*(d*x+c)+a*d-b*c)/(a*d-b*c))-a/b^2*ln(d*x+c)*ln((b*(d*x+c)+a*d-b*c)/(a*d-b*c))","A"
268,1,5,9,0.063000," ","int(ln(x)/(x-1),x)","-\dilog \left(x \right)"," ",0,"-dilog(x)","A"
269,1,77,43,0.066000," ","int(x*ln(-b*x-a+1)/(b*x+a),x)","\frac{x \ln \left(-b x -a +1\right)}{b}+\frac{a \dilog \left(-b x -a +1\right)}{b^{2}}+\frac{a \ln \left(-b x -a +1\right)}{b^{2}}-\frac{x}{b}-\frac{a}{b^{2}}-\frac{\ln \left(-b x -a +1\right)}{b^{2}}+\frac{1}{b^{2}}"," ",0,"1/b*ln(-b*x-a+1)*x+1/b^2*dilog(-b*x-a+1)*a+1/b^2*ln(-b*x-a+1)*a-1/b*x-1/b^2*ln(-b*x-a+1)-a/b^2+1/b^2","A"
270,1,31,28,0.073000," ","int((2*c*x+b)*ln(x)/x/(c*x+b),x)","\frac{\ln \left(x \right)^{2}}{2}+\ln \left(x \right) \ln \left(\frac{c x +b}{b}\right)+\dilog \left(\frac{c x +b}{b}\right)"," ",0,"1/2*ln(x)^2+ln(x)*ln((c*x+b)/b)+dilog((c*x+b)/b)","A"
271,1,8,7,0.079000," ","int(sin(x*ln(x))+ln(x)*sin(x*ln(x)),x)","-\cos \left(x \ln \left(x \right)\right)"," ",0,"-cos(x*ln(x))","A"
272,1,57,62,0.083000," ","int(ln((1-(x-1)^2)/(1+(x-1)^2))/x^2,x)","-\arctan \left(x -1\right)+\frac{\ln \left(x \right)}{2}+\frac{\ln \left(x -2\right)}{2}-\frac{\ln \left(x^{2}-2 x +2\right)}{2}-\frac{\ln \left(\frac{\left(-x +2\right) x}{x^{2}-2 x +2}\right)}{x}-\frac{1}{x}"," ",0,"-1/x*ln(x*(-x+2)/(x^2-2*x+2))+1/2*ln(x-2)-1/2*ln(x^2-2*x+2)-arctan(x-1)-1/x+1/2*ln(x)","A"
273,1,24,23,0.064000," ","int(ln(x+x^(1/2)),x)","x \ln \left(x +\sqrt{x}\right)-x -\ln \left(\sqrt{x}+1\right)+\sqrt{x}"," ",0,"-x-ln(x^(1/2)+1)+x*ln(x+x^(1/2))+x^(1/2)","A"
274,1,28,18,0.201000," ","int(ln(-1/(x+1)*x),x)","\ln \left(\frac{1}{x +1}\right)-\left(-1+\frac{1}{x +1}\right) \left(x +1\right) \ln \left(-1+\frac{1}{x +1}\right)"," ",0,"ln(1/(x+1))-ln(-1+1/(x+1))*(-1+1/(x+1))*(x+1)","A"
275,1,35,24,0.166000," ","int(ln((x-1)/(x+1)),x)","2 \ln \left(-\frac{2}{x +1}\right)+\left(1-\frac{2}{x +1}\right) \left(x +1\right) \ln \left(1-\frac{2}{x +1}\right)"," ",0,"2*ln(-2/(x+1))+ln(1-2/(x+1))*(1-2/(x+1))*(x+1)","A"
276,1,112,53,0.280000," ","int(ln((-x^2+1)/(x^2+1))/(x+1)^2,x)","-\frac{\ln \left(\frac{-x^{2}+1}{x^{2}+1}\right)}{x +1}+\frac{i x \ln \left(x -i\right)-x \ln \left(x -i\right)-i x \ln \left(x +i\right)-x \ln \left(x +i\right)+x \ln \left(x^{2}-1\right)+i \ln \left(x -i\right)-\ln \left(x -i\right)-i \ln \left(x +i\right)-\ln \left(x +i\right)+\ln \left(x^{2}-1\right)-2}{2 x +2}"," ",0,"-ln((-x^2+1)/(x^2+1))/(x+1)+1/2*(I*ln(x-I)*x-I*ln(x+I)*x+I*ln(x-I)-ln(x-I)*x-I*ln(x+I)-ln(x+I)*x+ln(x^2-1)*x-ln(x-I)-ln(x+I)+ln(x^2-1)-2)/(x+1)","C"
277,1,249,56,0.618000," ","int(ln(c*(x^2+1)^n)/(x^2+1),x)","-\frac{i \pi  \arctan \left(x \right) \mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i \left(x^{2}+1\right)^{n}\right) \mathrm{csgn}\left(i c \left(x^{2}+1\right)^{n}\right)}{2}+\frac{i \pi  \arctan \left(x \right) \mathrm{csgn}\left(i c \right) \mathrm{csgn}\left(i c \left(x^{2}+1\right)^{n}\right)^{2}}{2}+\frac{i \pi  \arctan \left(x \right) \mathrm{csgn}\left(i \left(x^{2}+1\right)^{n}\right) \mathrm{csgn}\left(i c \left(x^{2}+1\right)^{n}\right)^{2}}{2}-\frac{i \pi  \arctan \left(x \right) \mathrm{csgn}\left(i c \left(x^{2}+1\right)^{n}\right)^{3}}{2}-n \arctan \left(x \right) \ln \left(x^{2}+1\right)+\frac{i n \ln \left(-\frac{i \left(x +i\right)}{2}\right) \ln \left(x -i\right)}{2}-\frac{i n \ln \left(\frac{i \left(x -i\right)}{2}\right) \ln \left(x +i\right)}{2}+\frac{i n \ln \left(x -i\right)^{2}}{4}-\frac{i n \ln \left(x -i\right) \ln \left(x^{2}+1\right)}{2}-\frac{i n \ln \left(x +i\right)^{2}}{4}+\frac{i n \ln \left(x +i\right) \ln \left(x^{2}+1\right)}{2}+\frac{i n \dilog \left(-\frac{i \left(x +i\right)}{2}\right)}{2}-\frac{i n \dilog \left(\frac{i \left(x -i\right)}{2}\right)}{2}+\arctan \left(x \right) \ln \left(c \right)+\arctan \left(x \right) \ln \left(\left(x^{2}+1\right)^{n}\right)"," ",0,"arctan(x)*ln((x^2+1)^n)-n*ln(x^2+1)*arctan(x)-1/2*I*n*ln(x-I)*ln(x^2+1)+1/2*I*n*dilog(-1/2*I*(x+I))+1/2*I*n*ln(x-I)*ln(-1/2*I*(x+I))+1/4*I*n*ln(x-I)^2+1/2*I*n*ln(x+I)*ln(x^2+1)-1/2*I*n*dilog(1/2*I*(x-I))-1/2*I*n*ln(x+I)*ln(1/2*I*(x-I))-1/4*I*n*ln(x+I)^2+1/2*I*arctan(x)*Pi*csgn(I*(x^2+1)^n)*csgn(I*c*(x^2+1)^n)^2-1/2*I*arctan(x)*Pi*csgn(I*(x^2+1)^n)*csgn(I*c*(x^2+1)^n)*csgn(I*c)-1/2*I*arctan(x)*Pi*csgn(I*c*(x^2+1)^n)^3+1/2*I*arctan(x)*Pi*csgn(I*c*(x^2+1)^n)^2*csgn(I*c)+arctan(x)*ln(c)","C"
278,1,158,57,0.191000," ","int(ln(1/(x^2+1)*x^2)/(x^2+1),x)","i \ln \left(-i x \right) \ln \left(x -i\right)-i \ln \left(i x \right) \ln \left(x +i\right)-\frac{i \ln \left(-\frac{i \left(x +i\right)}{2}\right) \ln \left(x -i\right)}{2}+\frac{i \ln \left(\frac{i \left(x -i\right)}{2}\right) \ln \left(x +i\right)}{2}-\frac{i \ln \left(\frac{x^{2}}{x^{2}+1}\right) \ln \left(x -i\right)}{2}+\frac{i \ln \left(\frac{x^{2}}{x^{2}+1}\right) \ln \left(x +i\right)}{2}-\frac{i \ln \left(x -i\right)^{2}}{4}+\frac{i \ln \left(x +i\right)^{2}}{4}+i \dilog \left(-i x \right)-i \dilog \left(i x \right)-\frac{i \dilog \left(-\frac{i \left(x +i\right)}{2}\right)}{2}+\frac{i \dilog \left(\frac{i \left(x -i\right)}{2}\right)}{2}"," ",0,"-1/2*I*ln(x-I)*ln(1/(x^2+1)*x^2)-1/2*I*dilog(-1/2*I*(x+I))-1/2*I*ln(x-I)*ln(-1/2*I*(x+I))+I*dilog(-I*x)+I*ln(x-I)*ln(-I*x)-1/4*I*ln(x-I)^2+1/2*I*ln(x+I)*ln(1/(x^2+1)*x^2)+1/2*I*dilog(1/2*I*(x-I))+1/2*I*ln(x+I)*ln(1/2*I*(x-I))-I*dilog(I*x)-I*ln(x+I)*ln(I*x)+1/4*I*ln(x+I)^2","B"
279,-2,0,121,180.000000," ","int(ln(c*x^2/(b*x^2+a))/(b*x^2+a),x)","\int \frac{\ln \left(\frac{c \,x^{2}}{b \,x^{2}+a}\right)}{b \,x^{2}+a}\, dx"," ",0,"int(ln(c*x^2/(b*x^2+a))/(b*x^2+a),x)","F"
280,0,0,24,0.502000," ","int(ln(1+I*(-a*x+1)^(1/2)/(a*x+1)^(1/2))/(-a^2*x^2+1),x)","\int \frac{\ln \left(1+\frac{i \sqrt{-a x +1}}{\sqrt{a x +1}}\right)}{-a^{2} x^{2}+1}\, dx"," ",0,"int(ln(1+I*(-a*x+1)^(1/2)/(a*x+1)^(1/2))/(-a^2*x^2+1),x)","F"
281,0,0,24,0.507000," ","int(ln(1-I*(-a*x+1)^(1/2)/(a*x+1)^(1/2))/(-a^2*x^2+1),x)","\int \frac{\ln \left(1-\frac{i \sqrt{-a x +1}}{\sqrt{a x +1}}\right)}{-a^{2} x^{2}+1}\, dx"," ",0,"int(ln(1-I*(-a*x+1)^(1/2)/(a*x+1)^(1/2))/(-a^2*x^2+1),x)","F"
282,1,15,14,0.063000," ","int(ln(exp(b*x+a)),x)","\frac{\ln \left({\mathrm e}^{b x +a}\right)^{2}}{2 b}"," ",0,"1/2*ln(exp(b*x+a))^2/b","A"
283,1,27,26,0.158000," ","int(ln(exp(b*x^n+a)),x)","-\frac{b n \,x^{n +1}}{n +1}+x \ln \left({\mathrm e}^{b \,x^{n}+a}\right)"," ",0,"-b*n*x^(n+1)/(n+1)+x*ln(exp(b*x^n+a))","A"
284,1,34,22,0.062000," ","int(exp(x)*ln(b*exp(x)+a),x)","{\mathrm e}^{x} \ln \left(b \,{\mathrm e}^{x}+a \right)+\frac{a \ln \left(b \,{\mathrm e}^{x}+a \right)}{b}-{\mathrm e}^{x}-\frac{a}{b}"," ",0,"exp(x)*ln(b*exp(x)+a)-exp(x)+a*ln(b*exp(x)+a)/b-a/b","A"
285,1,26,24,0.623000," ","int(exp(b*x+a)*ln(x),x)","\frac{\Ei \left(1, -b x \right) {\mathrm e}^{a}}{b}+\frac{{\mathrm e}^{b x +a} \ln \left(x \right)}{b}"," ",0,"exp(b*x+a)*ln(x)/b+1/b*exp(a)*Ei(1,-b*x)","A"
286,0,0,12,0.077000," ","int(x^2/(x+ln(x)),x)","\int \frac{x^{2}}{x +\ln \left(x \right)}\, dx"," ",0,"int(x^2/(x+ln(x)),x)","F"
287,0,0,10,0.070000," ","int(x/(x+ln(x)),x)","\int \frac{x}{x +\ln \left(x \right)}\, dx"," ",0,"int(x/(x+ln(x)),x)","F"
288,0,0,8,0.069000," ","int(1/(x+ln(x)),x)","\int \frac{1}{x +\ln \left(x \right)}\, dx"," ",0,"int(1/(x+ln(x)),x)","F"
289,0,0,12,0.072000," ","int(1/x/(x+ln(x)),x)","\int \frac{1}{\left(x +\ln \left(x \right)\right) x}\, dx"," ",0,"int(1/x/(x+ln(x)),x)","F"
290,0,0,12,0.075000," ","int(1/x^2/(x+ln(x)),x)","\int \frac{1}{\left(x +\ln \left(x \right)\right) x^{2}}\, dx"," ",0,"int(1/x^2/(x+ln(x)),x)","F"
291,1,12,11,0.066000," ","int(ln(x)/(x+4*x*ln(x)^2),x)","\frac{\ln \left(4 \ln \left(x \right)^{2}+1\right)}{8}"," ",0,"1/8*ln(1+4*ln(x)^2)","A"
292,1,11,9,0.073000," ","int((1-ln(x))/x/(x+ln(x)),x)","-\ln \left(x \right)+\ln \left(x +\ln \left(x \right)\right)"," ",0,"-ln(x)+ln(x+ln(x))","A"
293,0,0,13,0.074000," ","int((x+1)/ln(x)/(x+ln(x)),x)","\int \frac{x +1}{\left(x +\ln \left(x \right)\right) \ln \left(x \right)}\, dx"," ",0,"int((x+1)/ln(x)/(x+ln(x)),x)","F"
294,1,108,53,0.145000," ","int(ln(2+((x+1)/x)^(1/2)),x)","x \ln \left(2+\sqrt{\frac{x +1}{x}}\right)+\frac{-3 \sqrt{\frac{x +1}{x}}\, x \ln \left(-3 x +1\right)-\sqrt{9}\, \sqrt{\left(x +1\right) x}\, \ln \left(\frac{15 x +4 \sqrt{9}\, \sqrt{x^{2}+x}+3}{9 x -3}\right)+6 \sqrt{\left(x +1\right) x}\, \ln \left(x +\frac{1}{2}+\sqrt{x^{2}+x}\right)}{18 \sqrt{\frac{x +1}{x}}\, x}"," ",0,"x*ln(2+((x+1)/x)^(1/2))+1/18/((x+1)/x)^(1/2)/x*(-9^(1/2)*ln(1/3*(4*9^(1/2)*(x^2+x)^(1/2)+15*x+3)/(3*x-1))*(x*(x+1))^(1/2)-3*((x+1)/x)^(1/2)*x*ln(1-3*x)+6*ln(x+1/2+(x^2+x)^(1/2))*(x*(x+1))^(1/2))","B"
295,-2,0,40,180.000000," ","int(ln(1+((x+1)/x)^(1/2)),x)","\int \ln \left(1+\sqrt{\frac{x +1}{x}}\right)\, dx"," ",0,"int(ln(1+((x+1)/x)^(1/2)),x)","F"
296,1,22,16,0.172000," ","int(1/2*ln((x+1)/x),x)","\frac{\left(\frac{1}{x}+1\right) x \ln \left(\frac{1}{x}+1\right)}{2}-\frac{\ln \left(\frac{1}{x}\right)}{2}"," ",0,"-1/2*ln(1/x)+1/2*ln(1/x+1)*(1/x+1)*x","A"
297,-2,0,40,180.000000," ","int(ln(-1+((x+1)/x)^(1/2)),x)","\int \ln \left(-1+\sqrt{\frac{x +1}{x}}\right)\, dx"," ",0,"int(ln(-1+((x+1)/x)^(1/2)),x)","F"
298,1,107,55,0.137000," ","int(ln(-2+((x+1)/x)^(1/2)),x)","x \ln \left(-2+\sqrt{\frac{x +1}{x}}\right)+\frac{-3 \sqrt{\frac{x +1}{x}}\, x \ln \left(-3 x +1\right)+\sqrt{9}\, \sqrt{\left(x +1\right) x}\, \ln \left(\frac{15 x +4 \sqrt{9}\, \sqrt{x^{2}+x}+3}{9 x -3}\right)-6 \sqrt{\left(x +1\right) x}\, \ln \left(x +\frac{1}{2}+\sqrt{x^{2}+x}\right)}{18 \sqrt{\frac{x +1}{x}}\, x}"," ",0,"x*ln(-2+((x+1)/x)^(1/2))+1/18/((x+1)/x)^(1/2)/x*(9^(1/2)*((x+1)*x)^(1/2)*ln(1/3*(15*x+4*9^(1/2)*(x^2+x)^(1/2)+3)/(3*x-1))-3*((x+1)/x)^(1/2)*x*ln(-3*x+1)-6*((x+1)*x)^(1/2)*ln(x+1/2+(x^2+x)^(1/2)))","A"
299,1,11,9,0.072000," ","int(x^(a*x)+x^(a*x)*ln(x),x)","\frac{{\mathrm e}^{a x \ln \left(x \right)}}{a}"," ",0,"1/a*exp(a*x*ln(x))","A"
300,0,0,27,0.275000," ","int((ln(x)^m)^p,x)","\int \left(\ln \left(x \right)^{m}\right)^{p}\, dx"," ",0,"int((ln(x)^m)^p,x)","F"
301,0,0,48,0.176000," ","int(ln(x)/(a+b*ln(x))^(1/2),x)","\int \frac{\ln \left(x \right)}{\sqrt{b \ln \left(x \right)+a}}\, dx"," ",0,"int(ln(x)/(a+b*ln(x))^(1/2),x)","F"
302,0,0,51,0.172000," ","int(ln(x)/(a-b*ln(x))^(1/2),x)","\int \frac{\ln \left(x \right)}{\sqrt{-b \ln \left(x \right)+a}}\, dx"," ",0,"int(ln(x)/(a-b*ln(x))^(1/2),x)","F"
303,0,0,57,0.148000," ","int((A+B*ln(x))/(b*ln(x)+a)^(1/2),x)","\int \frac{B \ln \left(x \right)+A}{\sqrt{b \ln \left(x \right)+a}}\, dx"," ",0,"int((A+B*ln(x))/(b*ln(x)+a)^(1/2),x)","F"
304,0,0,58,0.149000," ","int((B*ln(x)+A)/(-b*ln(x)+a)^(1/2),x)","\int \frac{B \ln \left(x \right)+A}{\sqrt{-b \ln \left(x \right)+a}}\, dx"," ",0,"int((B*ln(x)+A)/(-b*ln(x)+a)^(1/2),x)","F"
305,0,0,73,1.438000," ","int(x^2*ln(ln(x)*sin(x)),x)","\int x^{2} \ln \left(\ln \left(x \right) \sin \left(x \right)\right)\, dx"," ",0,"int(x^2*ln(ln(x)*sin(x)),x)","F"
306,0,0,60,1.333000," ","int(x*ln(ln(x)*sin(x)),x)","\int x \ln \left(\ln \left(x \right) \sin \left(x \right)\right)\, dx"," ",0,"int(x*ln(ln(x)*sin(x)),x)","F"
307,1,368,42,0.840000," ","int(ln(ln(x)*sin(x)),x)","-\frac{i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right)\right) \mathrm{csgn}\left(i \ln \left(x \right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right) \ln \left(x \right)\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right) \ln \left(x \right)\right)^{2}}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i {\mathrm e}^{-i x}\right) \mathrm{csgn}\left(\ln \left(x \right) \sin \left(x \right)\right)^{2}}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i {\mathrm e}^{-i x}\right) \mathrm{csgn}\left(\ln \left(x \right) \sin \left(x \right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right) \ln \left(x \right)\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i \ln \left(x \right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right) \ln \left(x \right)\right)^{2}}{2}+\frac{i \pi  x \mathrm{csgn}\left(\ln \left(x \right) \sin \left(x \right)\right)^{3}}{2}+\frac{i \pi  x \mathrm{csgn}\left(\ln \left(x \right) \sin \left(x \right)\right)^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right) \ln \left(x \right)\right)}{2}-\frac{i \pi  x \,\mathrm{csgn}\left(\ln \left(x \right) \sin \left(x \right)\right) \mathrm{csgn}\left(i \ln \left(x \right) \sin \left(x \right)\right)^{2}}{2}-\frac{i \pi  x \mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right) \ln \left(x \right)\right)^{3}}{2}-\frac{i \pi  x \mathrm{csgn}\left(i \ln \left(x \right) \sin \left(x \right)\right)^{3}}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(\ln \left(x \right) \sin \left(x \right)\right) \mathrm{csgn}\left(i \ln \left(x \right) \sin \left(x \right)\right)}{2}+\frac{i \pi  x \mathrm{csgn}\left(i \ln \left(x \right) \sin \left(x \right)\right)^{2}}{2}+\frac{i x^{2}}{2}-x \ln \left({\mathrm e}^{i x}\right)+x \ln \left(\ln \left(x \right)\right)+i \ln \left({\mathrm e}^{i x}+1\right) \ln \left({\mathrm e}^{i x}\right)-i \ln \left({\mathrm e}^{2 i x}-1\right) \ln \left({\mathrm e}^{i x}\right)-\frac{i \pi  x}{2}-\ln \left(2\right) x +\Ei \left(1, -\ln \left(x \right)\right)+i \dilog \left({\mathrm e}^{i x}+1\right)-i \dilog \left({\mathrm e}^{i x}\right)"," ",0,"-x*ln(exp(I*x))-1/2*I*Pi*csgn(I*(exp(2*I*x)-1))*csgn(I*ln(x))*csgn(I*ln(x)*(exp(2*I*x)-1))*x-1/2*I*Pi*x-I*dilog(exp(I*x))+1/2*I*Pi*csgn(ln(x)*sin(x))^3*x+I*ln(exp(I*x))*ln(exp(I*x)+1)-1/2*I*Pi*csgn(ln(x)*sin(x))*csgn(I*ln(x)*sin(x))^2*x-ln(2)*x-1/2*I*Pi*csgn(I*ln(x)*(exp(2*I*x)-1))^3*x-I*ln(exp(I*x))*ln(exp(2*I*x)-1)+1/2*I*Pi*csgn(I*ln(x)*(exp(2*I*x)-1))*csgn(ln(x)*sin(x))^2*x+1/2*I*Pi*csgn(I*ln(x))*csgn(I*ln(x)*(exp(2*I*x)-1))^2*x+1/2*I*Pi*csgn(I*(exp(2*I*x)-1))*csgn(I*ln(x)*(exp(2*I*x)-1))^2*x+1/2*I*x^2+1/2*I*Pi*csgn(I*exp(-I*x))*csgn(I*ln(x)*(exp(2*I*x)-1))*csgn(ln(x)*sin(x))*x+1/2*I*Pi*csgn(I*exp(-I*x))*csgn(ln(x)*sin(x))^2*x+1/2*I*Pi*csgn(I*ln(x)*sin(x))^2*x-1/2*I*Pi*csgn(I*ln(x)*sin(x))^3*x+1/2*I*Pi*csgn(ln(x)*sin(x))*csgn(I*ln(x)*sin(x))*x+I*dilog(exp(I*x)+1)+x*ln(ln(x))+Ei(1,-ln(x))","C"
308,0,0,12,3.178000," ","int(ln(ln(x)*sin(x))/x,x)","\int \frac{\ln \left(\ln \left(x \right) \sin \left(x \right)\right)}{x}\, dx"," ",0,"int(ln(ln(x)*sin(x))/x,x)","F"
309,0,0,25,3.264000," ","int(ln(ln(x)*sin(x))/x^2,x)","\int \frac{\ln \left(\ln \left(x \right) \sin \left(x \right)\right)}{x^{2}}\, dx"," ",0,"int(ln(ln(x)*sin(x))/x^2,x)","F"
310,0,0,76,2.473000," ","int(x^2*ln(exp(x)*ln(x)*sin(x)),x)","\int x^{2} \ln \left({\mathrm e}^{x} \ln \left(x \right) \sin \left(x \right)\right)\, dx"," ",0,"int(x^2*ln(exp(x)*ln(x)*sin(x)),x)","F"
311,0,0,63,2.354000," ","int(x*ln(exp(x)*ln(x)*sin(x)),x)","\int x \ln \left({\mathrm e}^{x} \ln \left(x \right) \sin \left(x \right)\right)\, dx"," ",0,"int(x*ln(exp(x)*ln(x)*sin(x)),x)","F"
312,1,583,45,1.045000," ","int(ln(exp(x)*ln(x)*sin(x)),x)","\frac{\ln \left({\mathrm e}^{x}\right)^{2}}{2}+\frac{i \pi  x \mathrm{csgn}\left(\ln \left(x \right) \sin \left(x \right)\right)^{3}}{2}-\frac{i \pi  x \mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right) \ln \left(x \right)\right)^{3}}{2}-\ln \left(2\right) x +\Ei \left(1, -\ln \left(x \right)\right)-\frac{i \pi  x \mathrm{csgn}\left(\left(-{\mathrm e}^{\left(1-i\right) x}+{\mathrm e}^{\left(1+i\right) x}\right) \ln \left(x \right)\right)^{3}}{2}-\frac{i \pi  x \mathrm{csgn}\left(i \left(-{\mathrm e}^{\left(1-i\right) x}+{\mathrm e}^{\left(1+i\right) x}\right) \ln \left(x \right)\right)^{3}}{2}+\frac{i \pi  x \mathrm{csgn}\left(\left(-{\mathrm e}^{\left(1-i\right) x}+{\mathrm e}^{\left(1+i\right) x}\right) \ln \left(x \right)\right)^{2}}{2}+i \ln \left({\mathrm e}^{i x}+1\right) \ln \left({\mathrm e}^{i x}\right)-i \ln \left({\mathrm e}^{2 i x}-1\right) \ln \left({\mathrm e}^{i x}\right)-\frac{i \pi  x}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i {\mathrm e}^{x}\right) \mathrm{csgn}\left(i \left(-{\mathrm e}^{\left(1-i\right) x}+{\mathrm e}^{\left(1+i\right) x}\right) \ln \left(x \right)\right)^{2}}{2}+\frac{i x^{2}}{2}-x \ln \left({\mathrm e}^{i x}\right)+i \dilog \left({\mathrm e}^{i x}+1\right)-i \dilog \left({\mathrm e}^{i x}\right)-\frac{i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right)\right) \mathrm{csgn}\left(i \ln \left(x \right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right) \ln \left(x \right)\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i {\mathrm e}^{-i x}\right) \mathrm{csgn}\left(\ln \left(x \right) \sin \left(x \right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right) \ln \left(x \right)\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i {\mathrm e}^{x}\right) \mathrm{csgn}\left(\ln \left(x \right) \sin \left(x \right)\right) \mathrm{csgn}\left(i \left(-{\mathrm e}^{\left(1-i\right) x}+{\mathrm e}^{\left(1+i\right) x}\right) \ln \left(x \right)\right)}{2}+x \ln \left(\ln \left(x \right)\right)+\frac{i \pi  x \mathrm{csgn}\left(\left(-{\mathrm e}^{\left(1-i\right) x}+{\mathrm e}^{\left(1+i\right) x}\right) \ln \left(x \right)\right)^{2} \mathrm{csgn}\left(i \left(-{\mathrm e}^{\left(1-i\right) x}+{\mathrm e}^{\left(1+i\right) x}\right) \ln \left(x \right)\right)}{2}-\frac{i \pi  x \,\mathrm{csgn}\left(\ln \left(x \right) \sin \left(x \right)\right) \mathrm{csgn}\left(i \left(-{\mathrm e}^{\left(1-i\right) x}+{\mathrm e}^{\left(1+i\right) x}\right) \ln \left(x \right)\right)^{2}}{2}-\frac{i \pi  x \,\mathrm{csgn}\left(\left(-{\mathrm e}^{\left(1-i\right) x}+{\mathrm e}^{\left(1+i\right) x}\right) \ln \left(x \right)\right) \mathrm{csgn}\left(i \left(-{\mathrm e}^{\left(1-i\right) x}+{\mathrm e}^{\left(1+i\right) x}\right) \ln \left(x \right)\right)}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right) \ln \left(x \right)\right)^{2}}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i {\mathrm e}^{-i x}\right) \mathrm{csgn}\left(\ln \left(x \right) \sin \left(x \right)\right)^{2}}{2}+\frac{i \pi  x \,\mathrm{csgn}\left(i \ln \left(x \right)\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right) \ln \left(x \right)\right)^{2}}{2}+\frac{i \pi  x \mathrm{csgn}\left(\ln \left(x \right) \sin \left(x \right)\right)^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right) \ln \left(x \right)\right)}{2}"," ",0,"1/2*ln(exp(x))^2-ln(2)*x+I*dilog(exp(I*x)+1)+Ei(1,-ln(x))-I*ln(exp(2*I*x)-1)*ln(exp(I*x))-1/2*I*Pi*csgn(I*ln(x)*(exp((1+I)*x)-exp((1-I)*x)))^3*x+1/2*I*x^2+1/2*I*Pi*x*csgn(ln(x)*sin(x))^3-1/2*I*Pi*x+I*ln(exp(I*x)+1)*ln(exp(I*x))+1/2*I*Pi*x*csgn(I*exp(-I*x))*csgn(ln(x)*sin(x))*csgn(I*(exp(2*I*x)-1)*ln(x))+1/2*I*Pi*csgn((exp((1+I)*x)-exp((1-I)*x))*ln(x))^2*x-1/2*I*Pi*csgn((exp((1+I)*x)-exp((1-I)*x))*ln(x))^3*x-1/2*I*Pi*x*csgn(I*(exp(2*I*x)-1)*ln(x))^3+1/2*I*Pi*csgn(I*exp(x))*csgn(ln(x)*sin(x))*csgn(I*ln(x)*(exp((1+I)*x)-exp((1-I)*x)))*x+1/2*I*Pi*csgn(I*ln(x)*(exp((1+I)*x)-exp((1-I)*x)))*csgn((exp((1+I)*x)-exp((1-I)*x))*ln(x))^2*x+1/2*I*Pi*csgn(I*exp(x))*csgn(I*ln(x)*(exp((1+I)*x)-exp((1-I)*x)))^2*x-x*ln(exp(I*x))-I*dilog(exp(I*x))+1/2*I*Pi*x*csgn(I*ln(x))*csgn(I*(exp(2*I*x)-1)*ln(x))^2+1/2*I*Pi*x*csgn(I*exp(-I*x))*csgn(ln(x)*sin(x))^2+1/2*I*Pi*x*csgn(ln(x)*sin(x))^2*csgn(I*(exp(2*I*x)-1)*ln(x))-1/2*I*Pi*x*csgn(I*(exp(2*I*x)-1))*csgn(I*ln(x))*csgn(I*(exp(2*I*x)-1)*ln(x))-1/2*I*Pi*csgn(I*ln(x)*(exp((1+I)*x)-exp((1-I)*x)))*csgn((exp((1+I)*x)-exp((1-I)*x))*ln(x))*x+x*ln(ln(x))-1/2*I*Pi*csgn(ln(x)*sin(x))*csgn(I*ln(x)*(exp((1+I)*x)-exp((1-I)*x)))^2*x+1/2*I*Pi*x*csgn(I*(exp(2*I*x)-1))*csgn(I*(exp(2*I*x)-1)*ln(x))^2","C"
313,0,0,14,4.235000," ","int(ln(exp(x)*ln(x)*sin(x))/x,x)","\int \frac{\ln \left({\mathrm e}^{x} \ln \left(x \right) \sin \left(x \right)\right)}{x}\, dx"," ",0,"int(ln(exp(x)*ln(x)*sin(x))/x,x)","F"
314,0,0,29,4.358000," ","int(ln(exp(x)*ln(x)*sin(x))/x^2,x)","\int \frac{\ln \left({\mathrm e}^{x} \ln \left(x \right) \sin \left(x \right)\right)}{x^{2}}\, dx"," ",0,"int(ln(exp(x)*ln(x)*sin(x))/x^2,x)","F"