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Question Number 112481 by bemath last updated on 08/Sep/20

$$\int \frac{\sin 2\mathrm{x}}{\sqrt{1+\cos {}^2\mathrm{x}}}\mathrm{dx}$$

Answered by john santu last updated on 08/Sep/20

$$\int \frac{2\sin x\cos x}{\sqrt{1+\cos {}^{2}x}}dx=\int -\frac{2udu}{\sqrt{1+u^2}}$$$$whereu=\cos x$$$$=-\int \frac{d(1+u^2)}{\sqrt{1+u^2}}=-2\sqrt{1+u^2}+c$$$$=-2\sqrt{1+\cos {}^{2}x}+c$$

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