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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

Integrate : $ \int \large\frac{\sin x}{1-\sin x}$$dx$

\[\begin {array} {1 1} (a)\;\sec x -\tan x +x+c \\ (b)\;-\sec x +\tan x -x+c \\ (c)\;\sec x+\tan x +x +c \\ (d)\;\sec x - \tan x -x +c \end {array}\]

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A)
$ \int \large\frac{\sin x(1+\sin x)}{(1-\sin x)(1+\sin x)}$$dx$
=> $ \int \large\frac{\sin x+\sin ^2 x)}{\cos^2 }$$dx$
=> $ \int \sec x \tan x +\tan ^2 x +dx$
=> $ \int \sec x \tan x +\sec^2 x +dx$
=> $ \sec x+\tan x-x +c$
Hence b is the correct answer
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