Question

evaluate the integral
int sin^{2}xcos xdx
int sin^{2}xcos xdx=square

Explanation:

Step1: Use substitution

Let $u = \sin x$, then $du=\cos xdx$.

Step2: Rewrite the integral

The integral $\int\sin^{2}x\cos xdx$ becomes $\int u^{2}du$.

Step3: Integrate using power - rule

The power - rule for integration is $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C$ ($n
eq - 1$). So, $\int u^{2}du=\frac{u^{3}}{3}+C$.

Step4: Substitute back

Substituting $u = \sin x$ back, we get $\frac{\sin^{3}x}{3}+C$.

Answer:

$\frac{\sin^{3}x}{3}+C$