(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

show

[tex]\int _1^{\infty }\frac{1}{x^2}\text{Log}[x]dx=-\int_0^1 \text{Log}[x] \, dx [/tex]

similarly show

[tex] \int _0^{\infty }\frac{1}{x^2+1}\text{Log}[x]dx = 0 [/tex]

3. The attempt at a solution

For the first part a substitution 1/x works.

The second part I cannot do, I thought about

[tex] \int _0^{\infty }\frac{1}{x^2+1}\text{Log}[x]dx=\int _1^{\infty }\frac{1}{x^2+1}\text{Log}[x]dx+\int _0^1\frac{1}{x^2+1}\text{Log}[x]dx [/tex]

and then trying to maybe show

[tex] \int _1^{\infty }\frac{1}{x^2+1}\text{Log}[x]dx=-\int _0^1\frac{1}{x^2+1}\text{Log}[x]dx [/tex]

but for now I am not sure what to do.

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# Homework Help: Improper integration change of variables

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