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प्रश्न
\[\int\sin x\sqrt{1 + \cos 2x} dx\]
बेरीज
उत्तर
` ∫ sin x \sqrt{ 1 + \text{cos 2 x dx} `
` = ∫ sin x . \sqrt{ 2cos ^2 x} dx ` ` [∴ 1 + cos 2x = 2 cos^2 X]`
\[ = \sqrt{2}\int\text{sin x }\text{cos x dx}\]
\[ = \frac{\sqrt{2}}{2}\int\text{2 }\text{sin x } \text{cos x dx}\]
\[ = \frac{1}{\sqrt{2}}\int\text{sin 2x dx}\]
\[ = \frac{1}{\sqrt{2}}\left[ \frac{- \cos 2x}{2} \right] + C\]
\[ = \frac{- 1}{2\sqrt{2}}\cos 2x + C\]
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