What is the integral of x^2e^{x+1} ?

The integral of x^2e^{x+1} is x^2e^{1+x}-2(e^{1+x}x-e^{1+x})+C

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integral of x^2e^{x+1}

\int x^{2} e^{x + 1} d x

x^{2} e^{1 + x} - 2 (e^{1 + x} x - e^{1 + x}) + C

Solution steps

\int x^{2} e^{x + 1} d x

Apply Integration By Parts

= x^{2} e^{1 + x} - \int 2 x e^{1 + x} d x

\int 2 x e^{1 + x} d x = 2 (e^{1 + x} x - e^{1 + x})

= x^{2} e^{1 + x} - 2 (e^{1 + x} x - e^{1 + x})

Add a constant to the solution

= x^{2} e^{1 + x} - 2 (e^{1 + x} x - e^{1 + x}) + C

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What is the integral of x^2e^{x+1} ?
The integral of x^2e^{x+1} is x^2e^{1+x}-2(e^{1+x}x-e^{1+x})+C