Answer
$-\frac{2}{3}(1+cos(t))^{3/2} +C$
Work Step by Step
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 $u$:
$-\frac{2}{3}(1+cos(t))^{3/2} +C$
