# Thread: Integration by trig substitution

1. ## Integration by trig substitution

Trying to do the indefinate integral of x^3 * (9-x^2)^1/2 by using the substitution of x = 3 sin u I get 81* integral[ (sin^3 u)(cos u)] but again I appear to be wrong.

2. $x = 3\sin u$
$dx = 3\cos u \: du$

$\int {\color{red}x^{3}} {\color{blue}\sqrt{9 -x^{2}}} {\color{magenta}dx}$
$= \int {\color{red}\left(3\sin u\right)^{3}} {\color{blue}\sqrt{9 - 9\cos^{2} u}} \cdot {\color{magenta}3 \cos u \: du}$
$= \int 27 \sin^{3} u \cdot 3 \sqrt{1 - \cos^{2} u} \cdot 3\cos u \: du$
$= 243 \int \sin^{4} u \cdot \cos u \: du$

I think you forgot to make the sub for dx. This last integral should be straightforward. Make the substitution s = sin u and you should be on your way

3. Thanks for that you are right I had forgot to sub in the dx value. How do you guys use the correct mathmatic symbols in the post?

4. Originally Posted by Craka
How do you guys use the correct mathmatic symbols in the post?
See the sticky in the LaTex help forum.