# Challenge: integral

#### greg1313

Forum Staff
Challenge:

$$\int\frac{x-1}{x+x^2\log(x)}\,dx$$

#### Joppy

Is it $b \tan^{-1}(x) + C$ for real b?

#### skipjack

Forum Staff
For $x$ > 0, $$\displaystyle \!\int\! \frac{x - 1}{x + x^2\ln(x)}\,dx = \!\int\!\left(\frac{1 + \ln(x)}{1 + x\ln(x)} - \frac{1}{x}\right)dx = \ln(1 + x\ln(x)) - \ln(x) + \mbox{C}$$, where $\mbox{C}$ is a constant.

2 people

#### Joppy

Would someone like to start a thread like this one?

i.e. post a challenging integral, whoever solves it posts another and so on.

1 person

#### greg1313

Forum Staff
I'm in. If skipjack's in, he can post the next one. If not, it's your turn, Joppy.

1 person

#### skipjack

Forum Staff
This isn't a good idea.

Forum Staff
Why not?

#### SDK

This seems like fun. It can't be less fun than reading about yet another disproof of Cantor or RH proof.

#### Joppy

Started a new thread here so it's clear for everyone.

#### skipjack

Forum Staff
It's very time-consuming and all the straightforward examples can be done by WolframAlpha.

Also, it encourages integrals to be posted where the result happens to be much more complicated than the integrand. These are often more tedious than interesting.