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,

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Stumbling Robot

A Fraction of a Dot
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Find the integral of * (log x)*^{2}

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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,

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|.

Please give easy way to solve it

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

This is the easiest way I guess

Ans is x(logx)^2 – x logo – x