Qual é a integral do $\int x ln x d x$ $int xlnx dx$ ?

$= \frac{x^{2}}{2} ln x - \frac{x^{2}}{4} + C$ $= x^2/2 ln x - x^2/4 + C$

nós usamos IBP

$\int u v' = u v - \int u' v$ $int u v' = uv - int u' v$

$u = ln x, u' = \frac{1}{x}$ $u = ln x, u' = 1/x$
$v' = x, v = \frac{x^{2}}{2}$ $v' = x, v = x^2/2$

$= \frac{x^{2}}{2} ln x - \int d x \frac{x}{2}$ $= x^2/2 ln x - int dx qquad x/2$

$= \frac{x^{2}}{2} ln x - \frac{x^{2}}{4} + C$ $= x^2/2 ln x - x^2/4 + C$

Qual é a integral do int xlnx dx ∫xlnxdxint xlnx dx ?