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

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

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integral of 2x^2e^x

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

y^{^{'}} = 1 + 9 x - 5 y, y (1) = 2

\frac{\partial}{\partial y} (ln (x^{2} + y^{2}))

\int \frac{9 x ^{2} + 5 x + 9}{( x ^{2} + 1 ) ^{2}} d x

ln (4 + x^{2})

\int_{1}^{2} 15 4 x^{2} - 3 d x

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