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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

\frac{d}{d x} ((2 x^{2} + x)^{200})

f (x) = \frac{y - 1}{3}

\frac{d}{d x} (\frac{5}{x} ln (x))

(tan (3 x))^{^{'}}

\int_{1}^{2} (1 - x^{2}) - (3 - 3 x) d x

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