What is the integral of x^2ln(ex) ?

The integral of x^2ln(ex) is 1/3 x^3ln(ex)-(x^3)/9+C

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integral of x^2ln(ex)

\int x^{2} ln (e x) d x

\frac{1}{3} x^{3} ln (e x) - \frac{x ^{3}}{9} + C

Solution steps

\int x^{2} ln (e x) d x

Apply Integration By Parts

: \frac{1}{3} x^{3} ln (e x) - \int \frac{x ^{2}}{3} d x

= \frac{1}{3} x^{3} ln (e x) - \int \frac{x ^{2}}{3} d x

\int \frac{x ^{2}}{3} d x = \frac{x ^{3}}{9}

= \frac{1}{3} x^{3} ln (e x) - \frac{x ^{3}}{9}

Add a constant to the solution

= \frac{1}{3} x^{3} ln (e x) - \frac{x ^{3}}{9} + C

y^{^{''}} - 4 y^{^{'}} + 4 y = t^{- 7} e^{2 t}

\int \frac{1}{( 1 - y ) ( 2 - y )} d y

f (s) = 2 t e^{- 5 t}

f (x) = x^{2} + 2 x, [1, 2]

\frac{d}{d x} (- 2 x^{2} + 2 x)

What is the integral of x^2ln(ex) ?
The integral of x^2ln(ex) is 1/3 x^3ln(ex)-(x^3)/9+C