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

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

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

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

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

Solution steps

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

\frac{d y}{d x} = \frac{x ^{3}}{y ^{2}}

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

\frac{d ^{3}}{d x ^{3}} (\frac{1}{x})

\int (5 x^{2} + 6 + \frac{7}{x ^{2} + 1}) d x

\frac{d}{d x} (- cosh (x))

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