What is the integral of e^xx^2 ?

The integral of e^xx^2 is x^2e^x-2(e^xx-e^x)+C

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integral of e^xx^2

\int e^{x} x^{2} d x

x^{2} e^{x} - 2 (e^{x} x - e^{x}) + C

Solution steps

\int e^{x} x^{2} d x

Apply Integration By Parts

: x^{2} e^{x} - \int 2 x e^{x} d x

= x^{2} e^{x} - \int 2 x e^{x} d x

\int 2 x e^{x} d x = 2 (e^{x} x - e^{x})

= x^{2} e^{x} - 2 (e^{x} x - e^{x})

Add a constant to the solution

= x^{2} e^{x} - 2 (e^{x} x - e^{x}) + C

\frac{1}{e ^{y}} y^{^{'}} = \frac{1}{e ^{x}}

\int \frac{x ^{3} - 8}{x - 2} d x

\frac{5}{12} (3 + 5) a^{3}

\int x^{2} + y^{5} d y

\frac{d}{d x} (\frac{x ^{2} - 2 e ^{x}}{x + 3 e ^{x}})