Question
Integrate the function: $\frac{\cos x}{\sqrt{1+\sin x}}$
✓
Answer
Let 1 + sinx = t
$\Rightarrow$ cosx dx = dt
$\Rightarrow \int \frac{\cos x}{\sqrt{1+\sin x}} d x=\int \frac{d t}{\sqrt{t}}$
$\Rightarrow \frac{t^{\frac{1}{2}}}{\frac{1}{2}}+C$
$\Rightarrow 2 \sqrt{t}+C$
$\Rightarrow 2 \sqrt{1+\sin x}+C$
$\Rightarrow$ cosx dx = dt
$\Rightarrow \int \frac{\cos x}{\sqrt{1+\sin x}} d x=\int \frac{d t}{\sqrt{t}}$
$\Rightarrow \frac{t^{\frac{1}{2}}}{\frac{1}{2}}+C$
$\Rightarrow 2 \sqrt{t}+C$
$\Rightarrow 2 \sqrt{1+\sin x}+C$
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