Answer
$\displaystyle\int\frac{\sin x}{\sqrt {(\cos x)}}$ dx = $-2\sqrt{(\cos x)}$ +c where c is an arbitrary constant
Work Step by Step
To solve this integral, we will attempt to find the derivative and antiderivative pair.
$\frac{d}{dx}(cosx)^{\frac{1}{2}}$=$\frac{1}{2}(cosx)^{-\frac{1}{2}}(-sinx)$
=-$\frac{sinx}{2\sqrt (cosx)}$
Therefore, $\int\frac{sinx}{\sqrt (cosθ)}$ dx = -2$\int-\frac{sinx}{2\sqrt (cosx)}$ dx
=-2$(cosx)^{\frac{1}{2}}$ +c
=-2$\sqrt(cosx)$ +c where c is an arbitrary constant
