## Calculus 8th Edition

$-\frac{2}{3}(1+cos(t))^{3/2} +C$
Evaluate the Integral using substitution: $\int sin(t)\sqrt{1+cos(t)}dt$ Substitution Rule: $\int f(g(x))g’(x)dx = \int f(u)du$ $u= 1+cos(t)$ $du =-sin(t)$ In this expression $du$ is multiplied by $-1$ to be $sin(t)$ Solve the integral in terms of $u$: $\int \sqrt{u}(-1)du$ $(-1)\int u^{1/2}du$ $(-1) \frac{2u^{3/2}}{3} +C$ Substitute for $u$: $-\frac{2}{3}(1+cos(t))^{3/2} +C$