Question Detail

To integrate $\cos^3 x$, we can rewrite it using the identity $\cos^2 x = 1 - \sin^2 x$:$\int \cos^3 x dx = \int \cos^2 x \cdot \cos x dx = \int (1 - \sin^2 x) \cos x dx$.Now, use u-substitution. Let $u = \sin x$, so $du = \cos x dx$.Substitute $u$ and $du$ into the integral:$\int (1 - u^2) du$Integrate with respect to $u$:$= u - \frac{u^3}{3} + C$.Substitute back $u = \sin x$:$= \sin x - \frac{1}{3}\sin^3 x + C$.