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

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

Popular >

integral of (x+2)e^{(x+2)}

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

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

Solution steps

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

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

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

Apply Integration By Parts

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

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

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

Expand

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

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

Add a constant to the solution

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

x \to 5 lim (\frac{x ^{2} + 1}{x + 1})

\int \frac{x}{36 x ^{2} + 9} d x

x \to 0 + lim ((1 + 3 x)^{\frac{1}{x}})

\frac{\partial}{\partial x} (- y - \frac{2 x}{y ^{3}})

\int \frac{ln ( x + 1 )}{( x + 1 )} d x

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