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

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

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integral of e^x(1-x^2)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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