# Homework Help: Find this integration

1. Oct 6, 2013

### utkarshakash

1. The problem statement, all variables and given/known data
$\displaystyle \int_0^1 \dfrac{xe^{tan^{-1}x}}{\sqrt{1+x^2}} dx$

2. Relevant equations

3. The attempt at a solution
Let tan^-1 (x) = t
x = tant
dt=dx/sqrt{1+x^2}
The integral then reduces to

$\displaystyle \int_0^{\pi/4} tante^tdt$

Applying integration by parts by taking tant as 1st function

$tant e^t - \displaystyle \int sec^2te^t dt$

This has made the problem more complicated instead of simplifying.

2. Oct 6, 2013

### Saitama

$$\frac{d}{dx}\left(\arctan(x)\right) ≠ \frac{1}{\sqrt{1+x^2}}$$
To use the substitution, multiply and divide by $\sqrt{1+x^2}$.