Question

integration of xlogx

Answer 1

Hey there!

Answer:


$I$ =$\int$x log x .dx


Solving by the 'integration by parts':


According to the 'ILATE' rule:


Let logx = 1st function and x be the second function.


Therefore,


= $log\:x \int x.dx - \int ( \frac{d(logx)}{dx}). \int x.dx).dx\\ \\ = log\:x \dfrac{x^{2}}{2} - \int(\dfrac{1}{x} .\dfrac{x^{2}}{2} ).dx\\ \\ = log\:x \: .\frac{x^{2}}{2} - \int (\dfrac{x}{2}).dx\\ \\ = log\:x\: . \dfrac{x^{2}}{2} - \dfrac{1}{2}.\frac{x^{2}}{2} \\ \\ = log\:x \: . \dfrac{x^{2}}{2} - \dfrac{x^{2}}{4}$


#Be Brainly.

Answer 2

$\huge{\bold{\red{Heya!!!}}}$



$\bold{\blue{Here\:is\:your\: answer\: }}$