Half Powered Integration

Calculus Level 4

\[\large\displaystyle \int \frac{1}{\sqrt{\sin^3 x \cos^5x}} \mathrm{d}x\]

The integral above is equals to \(a\tan^b x+c\tan^d x+ \text{constant} \). Where \(a,b,c,d\) are reals. Find the value of \(3(a+b+c+d)\).

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