Solve $\int \frac{1}{\sin ^{\frac{1}{2}}x \cos^{\frac{7}{2}}x}dx$ So it's given this indefinite integral $$\int \frac{1}{\sin ^{\frac{1}{2}}x \cos^{\frac{7}{2}}x}dx$$
Is there anyone could solve this integral? Thanks in advance.

Generalization:
$$\int\dfrac{dx}{\sin^ax\cos^{2b-a}x}=\int\dfrac{(1+\tan^2x)^{b-1}}{\tan^ax}\sec^2x\ dx$$
Set $\tan x=u$
