- #1

caffeinemachine

Gold Member

MHB

- 816

- 15

**Problem:**Evaluate

$$

\int_{0}^\infty \frac{e^{3x} - e^x}{x(e^x + 1)(e^{3x} + 1)}\ dx

$$

**Attempt.**

I substituted $y=e^x$, thus $dx = dy/y$, which turns the above integral to

$$

\int_{1}^\infty \frac{y^2 - 1}{(\log y)(y+1)(y^3+1)}\ dy = \int_{1}^\infty \frac{y-1}{(\log y) (y^3+1)} \ dy

$$

I am unable to make progress.

Thanks.