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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
Question
Evaluate $\int \frac{\cos ^2 x}{1+\sin x} d x$
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Answer

Let
$
\begin{array}{l}
I=\int \frac{\cos ^2 x}{1+\sin x} d x \\
I=\int \frac{1-\sin ^2 x}{1+\sin x} d x=\int \frac{(1-\sin x)(1+\sin x)}{1+\sin x} d x \\
I=\int(1-\sin x) d x=x+\cos x+\text { C }
\end{array}
$

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