What is the integral of (3-x^2)*e^x ?

The integral of (3-x^2)*e^x is -e^xx^2+2e^xx+e^x+C

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integral of (3-x^2)*e^x

\int (3 - x^{2}) \cdot e^{x} d x

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

Solution steps

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

Apply Integration By Parts

: e^{x} (3 - x^{2}) - \int - 2 e^{x} x d x

= e^{x} (3 - x^{2}) - \int - 2 e^{x} x d x

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

= e^{x} (3 - x^{2}) - (- 2 (e^{x} x - e^{x}))

Simplify

e^{x} (3 - x^{2}) - (- 2 (e^{x} x - e^{x})) : - e^{x} x^{2} + 2 e^{x} x + e^{x}

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

Add a constant to the solution

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

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What is the integral of (3-x^2)*e^x ?
The integral of (3-x^2)*e^x is -e^xx^2+2e^xx+e^x+C