Question

\[\int e^{cos^2 x}   \text{sin 2x  dx}\]

Answer 1

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