- #1

utkarshakash

Gold Member

- 855

- 13

## Homework Statement

[itex]\displaystyle \int_0^1 \dfrac{xe^{tan^{-1}x}}{\sqrt{1+x^2}} dx [/itex]

## Homework Equations

## The Attempt at a Solution

Let tan^-1 (x) = t

x = tant

dt=dx/sqrt{1+x^2}

The integral then reduces to

[itex]\displaystyle \int_0^{\pi/4} tante^tdt [/itex]

Applying integration by parts by taking tant as 1st function

[itex]tant e^t - \displaystyle \int sec^2te^t dt [/itex]

This has made the problem more complicated instead of simplifying.