Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - 8.3 Exercises - Page 530: 8

$2sin^{1/2}t-\frac 4 5 sin^{5/2}t+ \frac 2 9 sin^{9/2}t+C$

$\int \frac {cost(1-sin^2t)^2}{\sqrt {sint}}dt$ $u=sint, du=costdt$ $\int \frac {1-2u^2+u^4}{\sqrt u}du=\int u^{-1/2}-2u^{3/2}+u^{7/2}du$ $2u^{1/2}-\frac 4 5 u^{5/2}+\frac 2 9 u^{9/2}+C$ $2sin^{1/2}t-\frac 4 5 sin^{5/2}t+ \frac 2 9 sin^{9/2}t+C$