# Integration by Substition

1. Sep 27, 2011

### theRukus

1. The problem statement, all variables and given/known data
$\int \frac{-2x}{\sqrt[4]{x+2}}dx$

3. The attempt at a solution
$=-2*\int x(x+2)^{\frac{1}{4}}dx$

Let $u=x+2$.
Then, $u-2=x$,
and $du = dx$

.. Continued from above,
$=-2*\int (u-2)u^{\frac{1}{4}}du$
$=-2*\int u^{5/4}-2u^{\frac{1}{4}}du$

Is that last step allowed?

2. Sep 27, 2011

### Dick

Yes, absolutely. You are doing it exactly correctly.

3. Sep 28, 2011

### SteamKing

Staff Emeritus
Except the exponent (1/4) must be negative since the factor (x+2)^(1/4) was in the denominator in the OP.

4. Sep 28, 2011

### Dick

Ack. Missed that. Sorry.