Log-hyperbolic tangent integrals and Euler sums

A. Sofo

An investigation into the representation of integrals involving the product of the logarithm and the tanh^-1 functions will be undertaken in this paper. We will show that in many cases these integrals take an explicit form involving the Riemann Zeta function, the Dirichlet Eta function, Dirichlet Lambda function and many other special functions. Some examples illustrating the theorems will be detailed.