What is the integral of (x+1)^2*e^x ?

The integral of (x+1)^2*e^x is e^xx^2+e^x+C

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integral of (x+1)^2*e^x

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

e^{x} x^{2} + e^{x} + C

Solution steps

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

Apply Integration By Parts

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

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

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

Simplify

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

= e^{x} x^{2} + e^{x}

Add a constant to the solution

= e^{x} x^{2} + e^{x} + C

What is the integral of (x+1)^2*e^x ?
The integral of (x+1)^2*e^x is e^xx^2+e^x+C