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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

(x^{2} - 1) 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{\partial}{\partial x} (3 x^{2} + 9 y^{2} - x y + x)

\int \frac{x ^{3} + 5 x ^{4} - 7 x}{x ^{2}} d x

\int_{1}^{2} 5 x - 1 d x

\int_{- \infty}^{3} \frac{1}{x ^{2} + 9} d x

\frac{\partial}{\partial y} (\frac{6 x}{3 x ^{2} - y ^{3} - 3})

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