1,1,38,39,0.0136119,"\int x^2 \zeta (2,a+b x) \, dx","Integrate[x^2*Zeta[2, a + b*x],x]","\frac{b^2 x^2 \psi ^{(0)}(a+b x)-2 b x \text{log$\Gamma $}(a+b x)+2 \psi ^{(-2)}(a+b x)}{b^3}","\frac{2 \psi ^{(-2)}(a+b x)}{b^3}-\frac{2 x \text{log$\Gamma $}(a+b x)}{b^2}+\frac{x^2 \psi ^{(0)}(a+b x)}{b}",1,"(-2*b*x*LogGamma[a + b*x] + 2*PolyGamma[-2, a + b*x] + b^2*x^2*PolyGamma[0, a + b*x])/b^3","A",1
2,1,24,24,0.0098223,"\int x \zeta (2,a+b x) \, dx","Integrate[x*Zeta[2, a + b*x],x]","\frac{x \psi ^{(0)}(a+b x)}{b}-\frac{\text{log$\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",1
3,1,11,11,0.0039874,"\int \zeta (2,a+b x) \, dx","Integrate[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",1
4,0,0,14,0.0303352,"\int \frac{\zeta (2,a+b x)}{x} \, dx","Integrate[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,"Integrate[Zeta[2, a + b*x]/x, x]","F",-1
5,0,0,29,0.0248922,"\int \frac{\zeta (2,a+b x)}{x^2} \, dx","Integrate[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,"Integrate[Zeta[2, a + b*x]/x^2, x]","F",-1
6,0,0,51,0.0257839,"\int \frac{\zeta (2,a+b x)}{x^3} \, dx","Integrate[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,"Integrate[Zeta[2, a + b*x]/x^3, x]","F",-1
7,1,12,12,0.0294462,"\int \left(-\frac{b \psi ^{(2)}(a+b x)}{x}+\frac{\zeta (2,a+b x)}{x^2}\right) \, dx","Integrate[-((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",1
8,1,65,88,0.0316589,"\int x^2 \zeta (s,a+b x) \, dx","Integrate[x^2*Zeta[s, a + b*x],x]","-\frac{2 \zeta (s-3,a+b x)+b (s-3) x (2 \zeta (s-2,a+b x)+b (s-2) x \zeta (s-1,a+b x))}{b^3 (s-3) (s-2) (s-1)}","\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 + s)*x*(2*Zeta[-2 + s, a + b*x] + b*(-2 + s)*x*Zeta[-1 + s, a + b*x]))/(b^3*(-3 + s)*(-2 + s)*(-1 + s)))","A",1
9,1,40,50,0.0231697,"\int x \zeta (s,a+b x) \, dx","Integrate[x*Zeta[s, a + b*x],x]","-\frac{\zeta (s-2,a+b x)+b (s-2) x \zeta (s-1,a+b x)}{b^2 (s-2) (s-1)}","\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 + s)*x*Zeta[-1 + s, a + b*x])/(b^2*(-2 + s)*(-1 + s)))","A",1
10,1,20,20,0.0067835,"\int \zeta (s,a+b x) \, dx","Integrate[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
11,0,0,14,0.0224592,"\int \frac{\zeta (s,a+b x)}{x} \, dx","Integrate[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,"Integrate[Zeta[s, a + b*x]/x, x]","F",-1
12,0,0,33,0.0396217,"\int \frac{\zeta (s,a+b x)}{x^2} \, dx","Integrate[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,"Integrate[Zeta[s, a + b*x]/x^2, x]","F",-1
13,0,0,60,0.0336324,"\int \frac{\zeta (s,a+b x)}{x^3} \, dx","Integrate[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,"Integrate[Zeta[s, a + b*x]/x^3, x]","F",-1
14,1,12,12,0.0288084,"\int \left(\frac{\zeta (s,a+b x)}{x^2}+\frac{b s \zeta (1+s,a+b x)}{x}\right) \, dx","Integrate[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",1