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

Integrate : $\int \large\frac{x . \sin x}{1+ \cos x}$$dx$

$(a)\;\tan \frac{x}{2}+c \\(b)\;x. \tan (x/2)+c \\(c)\; \cot (x/2)+c \\ (d)\;None$

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A)
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$\int [xf'(x)+f(x) ]dx=x f(x) +c$
=> $\int \large\frac{x}{2} \sec^2 \large\frac{x}{2}$$+ \bigg(\tan \frac{x}{2}\bigg)$$dx$
=> $f(x) =\tan \large\frac{x}{2}$
=>$x. \tan (x/2)+c$
Hence b is the correct answer.
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