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CBSE Class 12 Maths 2010 Solved Paper

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Question : 1 of 29
Marks: +1, -0
Evaluate: ∫ log⁡xx\frac{\log x}{x} dx
Solution:  
I = ∫ log⁡xx\frac{\log x}{x} dx
Substitute log x = t
Differentiating w.r.t. x, we get
1x\frac{1}{x} dx = dt
On substitution, we get
I = ∫ log⁡xx\frac{\log x}{x} dx = ∫ t . dt = t22\frac{t^2}{2} + C = (log⁡x)22\frac{(\log x)^2}{2} + C
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