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

The integral of (x-5)^2e^x is e^xx^2-12e^xx+37e^x+C

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

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

e^{x} x^{2} - 12 e^{x} x + 37 e^{x} + C

Solution steps

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

Apply Integration By Parts

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

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

\int 2 (x - 5) e^{x} d x = 2 (e^{x} x - 6 e^{x})

= (x - 5)^{2} e^{x} - 2 (e^{x} x - 6 e^{x})

Simplify

(x - 5)^{2} e^{x} - 2 (e^{x} x - 6 e^{x}) : e^{x} x^{2} - 12 e^{x} x + 37 e^{x}

= e^{x} x^{2} - 12 e^{x} x + 37 e^{x}

Add a constant to the solution

= e^{x} x^{2} - 12 e^{x} x + 37 e^{x} + C

x \to 8 + lim (\frac{1}{( x - 8 ) ^{2}})

y^{^{'}} + 3 y = 3

5 x + 3 x

\frac{12 s}{( 132 s + 30 s ^{2} )}

y = 2 x, y = 4 x^{2}

What is the integral of (x-5)^2e^x ?
The integral of (x-5)^2e^x is e^xx^2-12e^xx+37e^x+C