The value of the integral is

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

The value of the integral

\int e^{\sin^2 x} (\cos x + \cos^3 x) \sin x \, dx

is (1)

\frac{1}{2} e^{\sin^2 x} (3 - \sin^2 x) + C

(2)

e^{\sin^2 x} \left(1 + \frac{1}{2} \cos^2 x\right) + C

(3)

e^{\sin^2 x} (3 \cos^2 x + 2 \sin^2 x) + C

(4)

e^{\sin^2 x} (2 \cos^2 x + 3 \sin^2 x) + C