INtergration of Sin

[girl4reehl]

Intergrate: (sin(x))^5

I got this far...

(sin(x))^4 * sinx dx
(1-(cos(x))^2)^2 * sinx dx
(1-2(cos(x))^2 + (cos(x))^4) * sinx dx
How do I go from there? brake up cos^4 ? or 2cos^2

I figured that my du=sin then my
u=cos! How? Help please.
Thanks!

 

[pka]

\(\displaystyle \L
\begin{array}{l}
\int {\sin ^4 (x)\sin (x)dx = \int {\left( {1 - 2\cos ^2 (x) + \cos ^4 (x)} \right)\sin (x)dx} } \\
= \int {\left( {1 - 2u^2 + u^4 } \right)du} \\
\end{array}\)

 

[girl4reehl]

Will that work?

 

[stapel]

Will that work?

Will what work? The u-substitution that you were given? If you're not sure, try it and see.

If you get stuck, please reply showing all of the steps you have tried. Thank you.

Eliz.