Find: $\int \cos^3 x e^{\ln \sin x} dx$
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $-\frac{\cos^4 x}{4} + C$
Let, $I = \int \cos^3 x e^{\ln \sin x} dx$
Or, $I = \int \cos^3 x \sin x dx$
Put, $\cos x = t ⇒-\sin x dx = dt$
$∴I = -\int t^3 dt$
Or, $I = -\frac{t^4}{4} + C$
Or, $I = -\frac{\cos^4 x}{4} + C$