- \( \int \sin(t) \sqrt{1 + \cos(t) } dt \)
- let \( u = 1 + \cos(t) \)
- \( \frac{du}{dt} = - \sin(t) \)
- \( dt = - \frac{1}{\sin(t)} du \)
- \( \int \sin(t) \cdot \frac{-1}{\sin(t)} \cdot u^{ \frac{1}{2} } du \)
- \( - \int u^{\frac{1}{2}} du\)
- \( - \frac{2}{3} u^{ \frac{3}{2} } + C \)
- \( - \frac{2}{3}( 1 + \cos(t))^{ \frac{3}{2} } + C\)
\( \int \sin(t) \sqrt{1 + \cos(t) } dt = - \frac{2}{3} ( 1 + \cos(t))^{ \frac{3}{2} } + C \)