Question

evaluate : integral of : xlog(x^2)​

Answer 1

Step-by-step explanation:

We have,

$\int \: x log( {x}^{2} ) dx$

Using integration by parts

$= log( {x}^{2} ) \int \: xdx - \int( \frac{d}{dx} ( log( {x}^{2} )) )\int \: xdx )dx$

$= \frac{ {x}^{2} }{2} log( {x}^{2} ) - \int( \frac{2x}{ {x}^{2} } \times \frac{ {x}^{2} }{2} )dx$

$= {x}^{2} log(( {x}^{2} )^{ \frac{1}{2} } ) - \int \: xdx$

$= {x}^{2} log(x) - \frac{ {x}^{2} }{2} + c$