1,1,39,0,0.0477429,"\int x^2 \zeta (2,a+b x) \, dx","Int[x^2*Zeta[2, a + b*x],x]","\frac{2 \psi ^{(-2)}(a+b x)}{b^3}-\frac{2 x \text{log$\Gamma $}(a+b x)}{b^2}+\frac{x^2 \psi ^{(0)}(a+b x)}{b}","\frac{2 \psi ^{(-2)}(a+b x)}{b^3}-\frac{2 x \text{log$\Gamma $}(a+b x)}{b^2}+\frac{x^2 \psi ^{(0)}(a+b x)}{b}",1,"(-2*x*LogGamma[a + b*x])/b^2 + (2*PolyGamma[-2, a + b*x])/b^3 + (x^2*PolyGamma[0, a + b*x])/b","A",4,3,11,0.2727,1,"{6583, 6571, 6567}"
2,1,24,0,0.0186062,"\int x \zeta (2,a+b x) \, dx","Int[x*Zeta[2, a + b*x],x]","\frac{x \psi ^{(0)}(a+b x)}{b}-\frac{\text{log$\Gamma $}(a+b x)}{b^2}","\frac{x \psi ^{(0)}(a+b x)}{b}-\frac{\text{log$\Gamma $}(a+b x)}{b^2}",1,"-(LogGamma[a + b*x]/b^2) + (x*PolyGamma[0, a + b*x])/b","A",3,3,9,0.3333,1,"{6583, 6571, 6570}"
3,1,11,0,0.0192677,"\int \zeta (2,a+b x) \, dx","Int[Zeta[2, a + b*x],x]","\frac{\psi ^{(0)}(a+b x)}{b}","\frac{\psi ^{(0)}(a+b x)}{b}",1,"PolyGamma[0, a + b*x]/b","A",2,2,7,0.2857,1,"{6581, 6570}"
4,0,0,0,0.0200685,"\int \frac{\zeta (2,a+b x)}{x} \, dx","Int[Zeta[2, a + b*x]/x,x]","\int \frac{\zeta (2,a+b x)}{x} \, dx","\text{Int}\left(\frac{\psi ^{(1)}(a+b x)}{x},x\right)",0,"Defer[Int][PolyGamma[1, a + b*x]/x, x]","N/A",0,0,0,0,-1,"{}"
5,0,0,0,0.0334763,"\int \frac{\zeta (2,a+b x)}{x^2} \, dx","Int[Zeta[2, a + b*x]/x^2,x]","\int \frac{\zeta (2,a+b x)}{x^2} \, dx","b \text{Int}\left(\frac{\psi ^{(2)}(a+b x)}{x},x\right)-\frac{\psi ^{(1)}(a+b x)}{x}",0,"-(PolyGamma[1, a + b*x]/x) + b*Defer[Int][PolyGamma[2, a + b*x]/x, x]","N/A",0,0,0,0,-1,"{}"
6,0,0,0,0.0515077,"\int \frac{\zeta (2,a+b x)}{x^3} \, dx","Int[Zeta[2, a + b*x]/x^3,x]","\int \frac{\zeta (2,a+b x)}{x^3} \, dx","\frac{1}{2} b^2 \text{Int}\left(\frac{\psi ^{(3)}(a+b x)}{x},x\right)-\frac{\psi ^{(1)}(a+b x)}{2 x^2}-\frac{b \psi ^{(2)}(a+b x)}{2 x}",0,"-PolyGamma[1, a + b*x]/(2*x^2) - (b*PolyGamma[2, a + b*x])/(2*x) + (b^2*Defer[Int][PolyGamma[3, a + b*x]/x, x])/2","N/A",0,0,0,0,-1,"{}"
7,1,12,0,0.0612303,"\int \left(-\frac{b \psi ^{(2)}(a+b x)}{x}+\frac{\zeta (2,a+b x)}{x^2}\right) \, dx","Int[-((b*PolyGamma[2, a + b*x])/x) + Zeta[2, a + b*x]/x^2,x]","-\frac{\psi ^{(1)}(a+b x)}{x}","-\frac{\psi ^{(1)}(a+b x)}{x}",1,"-(PolyGamma[1, a + b*x]/x)","A",3,2,25,0.08000,1,"{6583, 6572}"
8,1,88,0,0.0538692,"\int x^2 \zeta (s,a+b x) \, dx","Int[x^2*Zeta[s, a + b*x],x]","\frac{2 \zeta (s-3,a+b x)}{b^3 (1-s) (2-s) (3-s)}-\frac{2 x \zeta (s-2,a+b x)}{b^2 (1-s) (2-s)}+\frac{x^2 \zeta (s-1,a+b x)}{b (1-s)}","\frac{2 \zeta (s-3,a+b x)}{b^3 (1-s) (2-s) (3-s)}-\frac{2 x \zeta (s-2,a+b x)}{b^2 (1-s) (2-s)}+\frac{x^2 \zeta (s-1,a+b x)}{b (1-s)}",1,"(2*Zeta[-3 + s, a + b*x])/(b^3*(1 - s)*(2 - s)*(3 - s)) - (2*x*Zeta[-2 + s, a + b*x])/(b^2*(1 - s)*(2 - s)) + (x^2*Zeta[-1 + s, a + b*x])/(b*(1 - s))","A",3,2,11,0.1818,1,"{6584, 6582}"
9,1,50,0,0.0267418,"\int x \zeta (s,a+b x) \, dx","Int[x*Zeta[s, a + b*x],x]","\frac{x \zeta (s-1,a+b x)}{b (1-s)}-\frac{\zeta (s-2,a+b x)}{b^2 (1-s) (2-s)}","\frac{x \zeta (s-1,a+b x)}{b (1-s)}-\frac{\zeta (s-2,a+b x)}{b^2 (1-s) (2-s)}",1,"-(Zeta[-2 + s, a + b*x]/(b^2*(1 - s)*(2 - s))) + (x*Zeta[-1 + s, a + b*x])/(b*(1 - s))","A",2,2,9,0.2222,1,"{6584, 6582}"
10,1,20,0,0.0058214,"\int \zeta (s,a+b x) \, dx","Int[Zeta[s, a + b*x],x]","\frac{\zeta (s-1,a+b x)}{b (1-s)}","\frac{\zeta (s-1,a+b x)}{b (1-s)}",1,"Zeta[-1 + s, a + b*x]/(b*(1 - s))","A",1,1,7,0.1429,1,"{6582}"
11,0,0,0,0.0157624,"\int \frac{\zeta (s,a+b x)}{x} \, dx","Int[Zeta[s, a + b*x]/x,x]","\int \frac{\zeta (s,a+b x)}{x} \, dx","\text{Int}\left(\frac{\zeta (s,a+b x)}{x},x\right)",0,"Defer[Int][Zeta[s, a + b*x]/x, x]","N/A",0,0,0,0,-1,"{}"
12,0,0,0,0.0307605,"\int \frac{\zeta (s,a+b x)}{x^2} \, dx","Int[Zeta[s, a + b*x]/x^2,x]","\int \frac{\zeta (s,a+b x)}{x^2} \, dx","-b s \text{Int}\left(\frac{\zeta (s+1,a+b x)}{x},x\right)-\frac{\zeta (s,a+b x)}{x}",0,"-(Zeta[s, a + b*x]/x) - b*s*Defer[Int][Zeta[1 + s, a + b*x]/x, x]","N/A",0,0,0,0,-1,"{}"
13,0,0,0,0.051375,"\int \frac{\zeta (s,a+b x)}{x^3} \, dx","Int[Zeta[s, a + b*x]/x^3,x]","\int \frac{\zeta (s,a+b x)}{x^3} \, dx","\frac{1}{2} b^2 s (s+1) \text{Int}\left(\frac{\zeta (s+2,a+b x)}{x},x\right)-\frac{\zeta (s,a+b x)}{2 x^2}+\frac{b s \zeta (s+1,a+b x)}{2 x}",0,"-Zeta[s, a + b*x]/(2*x^2) + (b*s*Zeta[1 + s, a + b*x])/(2*x) + (b^2*s*(1 + s)*Defer[Int][Zeta[2 + s, a + b*x]/x, x])/2","N/A",0,0,0,0,-1,"{}"
14,1,12,0,0.0488385,"\int \left(\frac{\zeta (s,a+b x)}{x^2}+\frac{b s \zeta (1+s,a+b x)}{x}\right) \, dx","Int[Zeta[s, a + b*x]/x^2 + (b*s*Zeta[1 + s, a + b*x])/x,x]","-\frac{\zeta (s,a+b x)}{x}","-\frac{\zeta (s,a+b x)}{x}",1,"-(Zeta[s, a + b*x]/x)","A",2,1,27,0.03704,1,"{6585}"