Question

$\int \frac{\sin 5x}{\sqrt{\cos 5x}}d{x}_{=}$

• A. $\frac{2}{5}\sqrt{\cos 5x}+c$
• B. $\frac{-2}{5}\sqrt{\cos 5x}+c$
• C. $10\sqrt{\cos 5x}+c$
• D. $-10\sqrt{\cos 5x}+c$

Answer 1

Answer: (B)

$\frac{-2}{5}\sqrt{\cos 5x}+c$

Given, $\int \frac{\sin 5x}{\sqrt{\cos 5x}}dx$

Let $\cos 5x=t$

$-\sqrt{\sin }5xdx=dt$

$\sin 5xdx=\frac{-dt}{5}$

$\int \frac{-1}{\sqrt{t}}-\frac{dt}{5}=-2/5\sqrt{t}+c$

$=\frac{-2}{5}\sqrt{t}+c$

$=\frac{-2}{5}\sqrt{\cos 5x}+c$