Question

Integrate x*lnx

Please help :)

Answer 1

1/4 x^2 (2 ln x -1) +c

Answer 2

But how do you come to that solution? @Jack1

Answer 3

by part, let u = lnx dv =xdx
\[du = \frac{1}{x}dx\] \[v=\frac{x^2}{2}\]
\[\int{lnx*xdx}= \frac{x^2}{2}*lnx - \int{\frac{x^2}{2}*\frac{1}{x}dx}\]
\[= \frac{x^2lnx}{2} - \frac{x^2}{4}+C\]
hopefully no mistake.

Answer 4

@amistre64 check my stuff, please

Answer 5

Thank you, I understand what you have done now!
But why do you do it? Why do you subtract that part? @Loser66

Answer 6

because that's the formula when take integrate by part

Answer 7

by parts is fine

Answer 8

hey