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Question
Solution
\[\text{Let I} = \int e^\ cos^2 x \sin2x dx\]
\[ Let \cos^2 x = t\]
\[ \text{On differentiating both sides, we get}\]
\[ - \text{2 }\text{cos x sin x dx} = dt\]
\[ \therefore I = \int e^t 2 \sin x \cos x \frac{dt}{- 2 \sin x \cos x}\]
\[ = - \int e^t dt\]
\[ = - e^t + c\]
\[ = - e^\ cos^2 x + c\]
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