2
$\begingroup$

I am not even going to show my work because I have accomplished nothing attempting this problem. I have absolutely no idea what to do.

$\int \frac{\cos^5 x}{ \sqrt {\sin x}}\, dx$

  • 0
    This silly system should tell me that someone else is editing the post at the same time.2012-06-03

1 Answers 1

6

Write $\cos^{5}(x) = (1-\sin^{2}{x})^{2} \cdot \cos{x}$ and then put $t =\sin{x}$.

So you will have \begin{align*} \int \frac{\cos^{5}(x)}{\sqrt{\sin{x}}} \ dx &= \int \frac{(1-\sin^{2}(x))^{2}}{\sqrt{\sin{x}}} \cdot \cos{x} \ dx \\\ &=\int \frac{(1-t^{2})^{2}}{t^{1/2}} \ dt \\\ &=\int \frac{1-2t^{2}+t^{4}}{t^{1/2}} \ dt \end{align*}

Don't forget to then substitute u= t^(1/2) so du = (1/2)u^(-1/2)

  • 0
    @Jordan Not trying to put you down or anything but if memorization of tables is your strategy, I guarantee you before you reach the end of calculus you will be completely overwhelmed and you brain will be refused to crammed with useless boring formulas which it doesn't understand and doesn't know how/when to use. It takes patience, practice, and perseverance. That's it. No shortcuts!2012-12-07