Thread: Integration problem with trig functions and u-substitution

1. 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.

2. 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.
$\int {\frac{{\cos x}}{{{{\sin }^8}x}}} dx = \left\{ \begin{gathered}\sin x = u, \hfill \\\cos xdx = du \hfill \\ \end{gathered} \right\}$ $= \int {\frac{1}{{{u^8}}}} du = \int {{u^{ - 8}}} du = - \frac{{{u^{ - 7}}}}{7} + C = - \frac{1}{{7{u^7}}} + C = - \frac{1}{{7{{\sin }^7}x}} + C.$

3. Ah, I see. Thank you so much!