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