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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 : 24 of 271
Marks: +1, -0
(log⁡x)2x\frac{(\log x)^2}{x}
Solution:  
Let I=∫(log⁡x)2x dxI=\int \frac{(\log x)^2}{x}\,dx;
Put log⁡x=t\log x = t ⇒1x dx=dt\Rightarrow \frac{1}{x}\,dx = dt
I=∫t2 dt=t33+CI = \int t^2\,dt = \frac{t^3}{3} + C =13(log⁡x)3+C= \frac{1}{3}(\log x)^3 + C
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