What is the integral of e^x*x^2 ?

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

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integral of e^x*x^2

\int e^{x} \cdot 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

- 2 x^{3} + 17 x^{2} - 19 x - 14, [0, x]

\int \frac{cos ^{3} ( 4 x )}{sin ^{4} ( 4 x )} d x

\frac{d}{d x} ((x - \frac{1}{x})^{3})

\int \frac{7 x ^{3} + 7 x}{x - 1} d x

y^{^{'}} + 5 y = t + e^{- 2 t}

What is the integral of e^x*x^2 ?
The integral of e^x*x^2 is x^2e^x-2(e^xx-e^x)+C