Like Tony Stark
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- Apr 19, 2020
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[MATH]I=\int_0^1 Ln(\frac{1}{x})^{a-1} dx [/MATH]
With [MATH]a=2[/MATH] and [MATH]a=3[/MATH]
I differentiated both sides (because it converges uniformly), so I got:
[MATH]I'=\int_0^1 \frac{-a(-Ln(x)^{a-2})+(-Ln(x)^{a-2})}{x} dx [/MATH]
With that, I used u-substitution ([MATH]u=lnx[/MATH]) to get:
[MATH]I'=\int_\infty ^0 -a(-u^{a-2})+(-u^{a-2}) du [/MATH]
This is easy to integrate. But once it is solved, what should I do?
With [MATH]a=2[/MATH] and [MATH]a=3[/MATH]
I differentiated both sides (because it converges uniformly), so I got:
[MATH]I'=\int_0^1 \frac{-a(-Ln(x)^{a-2})+(-Ln(x)^{a-2})}{x} dx [/MATH]
With that, I used u-substitution ([MATH]u=lnx[/MATH]) to get:
[MATH]I'=\int_\infty ^0 -a(-u^{a-2})+(-u^{a-2}) du [/MATH]
This is easy to integrate. But once it is solved, what should I do?