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Question Number 36814 by MJS last updated on 06/Jun/18

$$\mathrm{now}\mathrm{the}\mathrm{way}\mathrm{is}\mathrm{clear},\mathrm{also}\mathrm{try}\mathrm{this}\mathrm{one}:$$$$\int \frac{\cos x}{{\sin }^{2}x\sqrt{\sin 2x}}dx$$

Answered by math1967 last updated on 06/Jun/18

$$\frac{1}{\sqrt{2}}\int \frac{cosx}{{sin}^{2}x\sqrt{\sin x\cos x}}dx$$$$=\frac{1}{\sqrt{2}}\int \sqrt{cotx}\mathrm{cosec}{}^{2}xdx$$$$=-\frac{1}{\sqrt{2}}\int \sqrt{cotx}d\left(cotx\right)$$$$=-\frac{1}{\sqrt{2}}\times \frac{2}{3}\times {\left(cotx\right)}^{\frac{3}{2}}+c$$

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