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# Find the integral of (log x)2

Evaluate the following integral:

We use integration by parts, defining

First, we recall that was computed in Example 2 on p. 235 of Apostol which gave

Then we have,

1. Anonymous says:

Can you please explain this in a more easier way and elaborately

• Anonymous says:

Probably too late, but I solved it using integration by parts with both u = dv = log x

2. Artem says:

Why does the answer put an absolute sign in the answer? I think there is a mistake in Apostol answers – the answer should be clearly in terms of log(x) instead of log|x|, since x>0 due to the way the problem is defined. cannot accept negative x by default, only can. Thus, the integration bounds have to be strictly positive. Also the derivation of Apostol on page 235 is in terms of x, not |x|.

3. Manav says:

Please give easy way to solve it

4. Nitesh Pandey says:

Not satisfied by this solution please solve it in easy way that can be understood easily using formula
( “|” it willl be the sign of integration because there is no actual sign of integratio in mobile phones so please be understood)
Formula:-
u|vdx-(|du/dx |vdx) dx
This formula is given in elements maths of 12th class.
Thank You
Nitesh Pandey

• Anonymous says:

This is the easiest way I guess

• Dhruvan says:

Ans is x(logx)^2 – x logo – x