甽2. Find $\int \frac{1}{\sqrt{\sin ^{3} x \cdot \cos ^{5} x}} \mathrm{dx}$.

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2. Find $\int \frac{1}{\sqrt{\sin ^{3} x \cdot \cos ^{5} x}} \mathrm{dx}$.
$$
\begin{array}{l}
=\int \frac{\sin ^{2} x d x}{\sqrt{\sin ^{3} x \cdot \cos ^{5} x}}+\int \frac{\cos ^{2} x d x}{\sqrt{\sin ^{3} x \cdot \cos ^{5} x}} \\
=\int \frac{\sin ^{2} x d x}{\cos ^{4} x \sqrt{\tan ^{3} x}}+\int \frac{\cos ^{2} x d x}{\sin ^{4} x \sqrt{\cot ^{5} x}} \\
=\int \sqrt{\tan x} d(\tan x)-\int(\cot x)^{-\frac{1}{2}} d(\cot x) \\
=\frac{2}{3} \tan ^{\frac{3}{2}} x-2 \sqrt{\cot x}+C . \\
\end{array}
$$