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NCERT Class XII Mathematics Chapter - - Solutions

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Exercise - 7.2
Integrate the functions in Exercises 23 to 59.
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Question : 51 of 271
Marks: +1, -0
cot⁡xlog⁡sin⁡x\cot x \log \sin x
Solution:  
Let I=∫cot⁡xlog⁡sin⁡x dxI = \int \cot x \log \sin x \, dx
Put log⁡sin⁡x=t\log \sin x = t
⇒1sin⁡xcos⁡x dx=dt\Rightarrow \frac{1}{\sin x} \cos x \, dx = dt
⇒cot⁡x dx=dt\Rightarrow \cot x \, dx = dt
∴I=∫t dt=t22+C\therefore I = \int t \, dt = \frac{t^2}{2} + C =12(log⁡sin⁡x)2+C= \frac{1}{2} (\log \sin x)^2 + C
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