# Indefinite Integral – A quotient of functions with cos and sin – Exercise 2250

Exercise

Evaluate the integral

$$\int \frac{\cos^7 x}{\sqrt{\sin x}} dx$$

$$\int \frac{\cos^7 x}{\sqrt{\sin x}} dx =2\sqrt{\sin x}(1-\frac{3}{5}\sin^2 x+\frac{1}{3}\sin^4 x-\frac{1}{13}\sin^6 x)+c$$