- #1

Zoe-b

- 98

- 0

## Homework Statement

Find the integral of x over ((1+x)

^{1/2}-(1+x)

^{1/3}) dx

## Homework Equations

integration by substitution.

## The Attempt at a Solution

I have tried the substitution u = (1+x)

^{5/6}but not really sure if this makes it any better!

du/dx = 5/6 * (1+x)

^{-1/6}

6/5 * du = (1+x)

^{-1/6}dx

(1+x) = u

^{6/5}

x= u

^{6/5}- 1

Take a factor of (1+x)

^{1/6}of the denominator and rewrite to give:

6/5 * integral of (u

^{6/5}- 1)/(u

^{2/5}- u

^{1/5}) du

Is is possible to integrate this? Or do I need a completely different substitution?

Thanks.