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) \cdot 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

= (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

y = 10 x sin (x), (\frac{π}{2}, 5 π)

\int 3 arctan (x) d x

\frac{d}{d x} (sin (x^{2} + 1))

f (x) = \frac{2}{x}, (4, \frac{1}{2})

\frac{d}{d x} (1 + 2 cos (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