Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
Evaluate: $\int \frac{\sin x}{1+\sin x} d x$
A
$\sec x-\tan x+C$
B
$\sec x+\tan x+x+C$
C
$\sec x+\tan x+C$
✓
$\sec x-\tan x+x+C$
✓
Answer
Correct option: D.
$\sec x-\tan x+x+C$
(d) : Let $I=\int \frac{\sin x}{1+\sin x} d x=\int \frac{\sin x(1-\sin x)}{(1+\sin x)(1-\sin x)} d x$ $=\int \frac{\sin x-\sin ^2 x}{\cos ^2 x} d x=\int \sec x \tan x d x-\int \tan ^2 x d x$ $=\int \sec x \tan x d x-\int\left(\sec ^2 x-1\right) d x=\sec x-\tan x+x+C$
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