What is the integral of (x^2-5x)e^x ?

The integral of (x^2-5x)e^x is e^xx^2-7e^xx+7e^x+C

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integral of (x^2-5x)e^x

\int (x^{2} - 5 x) e^{x} d x

e^{x} x^{2} - 7 e^{x} x + 7 e^{x} + C

Solution steps

\int (x^{2} - 5 x) e^{x} d x

Apply Integration By Parts

= (x^{2} - 5 x) e^{x} - \int (2 x - 5) e^{x} d x

\int (2 x - 5) e^{x} d x = 2 e^{x} x - 7 e^{x}

= (x^{2} - 5 x) e^{x} - (2 e^{x} x - 7 e^{x})

Simplify

(x^{2} - 5 x) e^{x} - (2 e^{x} x - 7 e^{x}) : e^{x} x^{2} - 7 e^{x} x + 7 e^{x}

= e^{x} x^{2} - 7 e^{x} x + 7 e^{x}

Add a constant to the solution

= e^{x} x^{2} - 7 e^{x} x + 7 e^{x} + C

5 x - 4 y x^{2} + 1 \frac{d y}{d x} = 0

\frac{\partial}{\partial x} (2 x^{2} yz)

\frac{d}{d x} (ln (5 x^{2} + 6))

\frac{\partial}{\partial y} (x y + z)

y = x^{2} ln (7 x)

What is the integral of (x^2-5x)e^x ?
The integral of (x^2-5x)e^x is e^xx^2-7e^xx+7e^x+C