If $\int \frac{d x}{\sqrt{\sin ^3 x \cos x}}=g(x)+c$, then $g(x)$ is equal to

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Aicharya · Accepted Answer

Given, $\int \frac{d x}{\sqrt{\sin ^3 x \cos x}}=g(x)+c$ $ 	ext { Now, } \begin{aligned} \int \frac{d x}{\sqrt{\sin ^4 x \cot x}} & =\int \frac{d x}{\sin ^2 x \sqrt{\cot x}} \ & =\int \frac{\operatorname{cosec}^2 x}{\sqrt{\cot x}} d x \end{aligned} $ Put $\quad \cot x=t$ $ \begin{array}{rlrl} \Rightarrow-\operatorname{cosec}^2 x d x & =d t \ 	herefore \quad \int-\frac{1}{\sqrt{t}} d t & =-\frac{t^{1 / 2}}{1 / 2}+c \ & =-2 \sqrt{\cot x}+c \ & =-\frac{2}{\sqrt{	an x}}+c \ 	herefore & g(x) & =-\frac{2}{\sqrt{	an x}} \end{array} $

If $\int \frac{d x}{\sqrt{\sin ^3 x \cos x}}=g(x)+c$, then $g(x)$ is equal to

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