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Problem The value of the integral ∫ e sin 2 x ( cos x + cos 3 x ) sin x d x \int e^{\sin^2 x} (\cos x + \cos^3 x) \sin x \, dx ∫ e s i n 2 x ( cos x + cos 3 x ) sin x d x 1 2 e sin 2 x ( 3 − sin 2 x ) + C \frac{1}{2} e^{\sin^2 x} (3 - \sin^2 x) + C 2 1 e s i n 2 x ( 3 − sin 2 x ) + C e sin 2 x ( 1 + 1 2 cos 2 x ) + C e^{\sin^2 x} \left(1 + \frac{1}{2} \cos^2 x\right) + C e s i n 2 x ( 1 + 2 1 cos 2 x ) + C e sin 2 x ( 3 cos 2 x + 2 sin 2 x ) + C e^{\sin^2 x} (3 \cos^2 x + 2 \sin^2 x) + C e s i n 2 x ( 3 cos 2 x + 2 sin 2 x ) + C e sin 2 x ( 2 cos 2 x + 3 sin 2 x ) + C e^{\sin^2 x} (2 \cos^2 x + 3 \sin^2 x) + C e s i n 2 x ( 2 cos 2 x + 3 sin 2 x ) + C Browse the problem library