calculus - Evaluation of $int frac{sqrt{sin ^4x+cos ^4x}}{sin ^3x cos x }dx$

Evaluate the following integral:

$$\int \frac{\sqrt{\sin ^4x+\cos ^4x}}{\sin ^3x \cos x }dx$$ where $x \in \big(0,\frac{\pi}{2} \big)$

Could some give me hint as how to approach this question?

I tried to use the fact that $\sin ^4x+\cos ^4x=1-\frac{sin^22x}{2}$ but it didn't help. How should I proceed?