intergration Help!! (2 Viewers)

[Currybear]

How do i integrate

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x(ln x)^2

 

[Trebla]

How do i integrate

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x(ln x)^2

Multiple IBP and differentiate the log function on each occasion.

 

[cineti970128]

let g(x) = ln(x)^2
g'(x) = 2(ln(x))/x

f(x)= x
F(x) = 1/2x^2

integrating by parts
Integral(xln(x)^2) = 1/2x^2 * ln(x)^2 - Integral (xln(x)^2)

2Integral(xln(x)^2) = 1/2x^2 * ln(x)^2

Integral(xln(x)^2) = 1/4x^2 *ln(x)^2