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

Integrate : $\int \large\frac{1- x \sin x +\cos x }{x(1- \cos x )}$$dx$

$(a)\;\log _e |x (1+\sin x)|+c \\(b)\;\log _e |x (1+\cos x)|+c \\(c)\;\log _e |\cos x|+c \\ (d)\;None$

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A)
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$x(1+ \cos x )=t$
$x+ x \cos x =t$
differentiate with respect to x
$(1+\cos x - x \sin x )dx=dt$
$\qquad= \int \large\frac{dt}{t}$
$\qquad= \log _e|t|+c$
$\log _e |x (1+\cos x)|+c$
Hence b is the correct answer.
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