Integral calculus .

Question

This is a wonderful integral .already been able to find some steps to solve it but always incomplete . The integral is stated below. $$ \int_0^1 \frac{\mbox{arcsinh}(x)}{1+x^2} dx$$ Need a nice soln , i have a wonderful feeling it will be complex.hint; why not transforming the inverse hyperbolic function to a logarithmic function that would have make our work easier , i also tried that but not efficent to finish my soln. But trying it using differentiation under sign might also work during this case.

Answer 1

Running the integral in Maple gives

$$\int_0^1 \frac{\mbox{arcsinh}(x)}{1+x^2} dx=$$

Only posting this as a bit of information, not attempt at solution.