I'm interested in integrals of the form
I(a,b)=∫
∞
0
arccot(x)⋅arccot(ax)⋅arccot(bx) dx, for a>0,b>0
It's known†Gradshteyn & Ryzhik, Table of Integrals, Series, and Products, 7th edition, page 599, (4.511) that
I(a,0)=
π2
4
[ln(1+
1
a
)+
ln(1+a)
a
].
Maple and Mathematica are also able to evaluate
I(1,1)=
3π2
4
ln2−
21
8
ζ(3).
