What is the integral of xe^{(x+2)} ?

The integral of xe^{(x+2)} is e^2(e^xx-e^x)+C

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integral of xe^{(x+2)}

\int x e^{(x + 2)} d x

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

Solution steps

\int x e^{x + 2} d x

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

= \int e^{2} x e^{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{2} \cdot \int x e^{x} d x

Apply Integration By Parts

: e^{x} x - \int e^{x} d x

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

\int e^{x} d x = e^{x}

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

Add a constant to the solution

= e^{2} (e^{x} x - e^{x}) + C

y^{^{''}} + 7 y^{^{'}} + 10 y = 0

\int - sinh (x) d x

\frac{d}{d x} (7 x + s + 9)

f (x) = \frac{x ^{2} - 1}{x}

\frac{d}{d x} (\frac{1}{4} x^{4} - \frac{2}{3} x^{3} + 2)

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