Question

Use integration by parts to find the integrals in Exercise. ∫x ln x dx.

Answer 1

Answer:

$I= \frac{x^2}{2}lnx- \frac{x^2}{4}+c$

Step-by-step explanation:

We have given expression $\int xln xdx$

Now integrating by part

$I=lnx\int x-\int \frac{d}{dx}lnx\int x$

$I=lnx\times \frac{x^2}{2}-\int \frac{1}{x}\times \frac{x^2}{2}$

$I=lnx\times \frac{x^2}{2}-\int \frac{x}{2}$

$I= \frac{x^2}{2}lnx- \frac{x^2}{4}+c$

So integral of the expression will be $\frac{x^2}{2}lnx- \frac{x^2}{4}+c$