What is the integral of xe^xln(x) ?

The integral of xe^xln(x) is e^xxln(x)-e^xln(x)-e^x+\Ei(x)+C

Popular >

integral of xe^xln(x)

\int x e^{x} ln (x) d x

e^{x} x ln (x) - e^{x} ln (x) - e^{x} + Ei (x) + C

Solution steps

\int x e^{x} ln (x) d x

Apply Integration By Parts

: ln (x) (e^{x} x - e^{x}) - \int \frac{e ^{x} x - e ^{x}}{x} d x

= ln (x) (e^{x} x - e^{x}) - \int \frac{e ^{x} x - e ^{x}}{x} d x

\int \frac{e ^{x} x - e ^{x}}{x} d x = e^{x} - Ei (x)

= ln (x) (e^{x} x - e^{x}) - (e^{x} - Ei (x))

Simplify

ln (x) (e^{x} x - e^{x}) - (e^{x} - Ei (x)) : e^{x} x ln (x) - e^{x} ln (x) - e^{x} + Ei (x)

= e^{x} x ln (x) - e^{x} ln (x) - e^{x} + Ei (x)

Add a constant to the solution

= e^{x} x ln (x) - e^{x} ln (x) - e^{x} + Ei (x) + C

\int 4 x^{\frac{1}{3}} + 4 x^{- \frac{1}{3}} d x

\int x^{5} - 3 x d x

\int \frac{( x ^{2} - 4 )}{x ^{2}} d x

\int \frac{2 x + 2}{x ^{2} + 2 x - 3} d x

\int e^{x} (3 + 3 e^{x})^{4} d x

What is the integral of xe^xln(x) ?
The integral of xe^xln(x) is e^xxln(x)-e^xln(x)-e^x+\Ei(x)+C