# Integration problem with trig functions and u-substitution

• January 19th 2009, 11:28 AM
Dana_Scully
Integration problem with trig functions and u-substitution
Hey, I'm having trouble figuring out where to go with this problem:

$\int \frac{\cos(x)}{\sin(x)^8} dx$

What would u be? I'm really bad with trig functions.
• January 19th 2009, 11:39 AM
DeMath
Quote:

Originally Posted by Dana_Scully
Hey, I'm having trouble figuring out where to go with this problem:

$\int \frac{\cos(x)}{\sin(x)^8} dx$

What would u be? I'm really bad with trig functions.

$\int {\frac{{\cos x}}{{{{\sin }^8}x}}} dx = \left\{ \begin{gathered}\sin x = u, \hfill \\\cos xdx = du \hfill \\ \end{gathered} \right\}$ $= \int {\frac{1}{{{u^8}}}} du = \int {{u^{ - 8}}} du = - \frac{{{u^{ - 7}}}}{7} + C = - \frac{1}{{7{u^7}}} + C = - \frac{1}{{7{{\sin }^7}x}} + C.$
• January 19th 2009, 11:45 AM
Dana_Scully
Ah, I see. Thank you so much!