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

The integral of xe^{(-2x)} is 1/4 (-2e^{-2x}x-e^{-2x})+C

Popular >

integral of xe^{(-2x)}

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

\frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x}) + C

Solution steps

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

Apply u-substitution

: \int \frac{e ^{u} u}{4} d u

= \int \frac{e ^{u} u}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int e^{u} u d u

Apply Integration By Parts

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

= \frac{1}{4} (e^{u} u - \int e^{u} d u)

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

= \frac{1}{4} (e^{u} u - e^{u})

Substitute back

u = - 2 x

= \frac{1}{4} (e^{- 2 x} (- 2 x) - e^{- 2 x})

Simplify

= \frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x})

Add a constant to the solution

= \frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x}) + C

\int (ln (7 x))^{2} d x

\int_{0}^{x^{2}} e^{t^{2}} d t

t \to 2 lim (\frac{t + 2}{t ^{2} - 4})

x \to \infty lim (- 2 x - 1)

f (x) = \frac{2}{x - 8}, at x = 10

What is the integral of xe^{(-2x)} ?
The integral of xe^{(-2x)} is 1/4 (-2e^{-2x}x-e^{-2x})+C