What is the integral of xe^{-10x} ?

The integral of xe^{-10x} is 1/100 (-10e^{-10x}x-e^{-10x})+C

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integral of xe^{-10x}

\int x e^{- 10 x} d x

\frac{1}{100} (- 10 e^{- 10 x} x - e^{- 10 x}) + C

Solution steps

\int x e^{- 10 x} d x

Apply u-substitution

: \int \frac{e ^{u} u}{100} d u

= \int \frac{e ^{u} u}{100} d u

Take the constant out:

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

= \frac{1}{100} \cdot \int e^{u} u d u

Apply Integration By Parts

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

= \frac{1}{100} (e^{u} u - \int e^{u} d u)

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

= \frac{1}{100} (e^{u} u - e^{u})

Substitute back

u = - 10 x

= \frac{1}{100} (e^{- 10 x} (- 10 x) - e^{- 10 x})

Simplify

= \frac{1}{100} (- 10 e^{- 10 x} x - e^{- 10 x})

Add a constant to the solution

= \frac{1}{100} (- 10 e^{- 10 x} x - e^{- 10 x}) + C

\int cos (4 x) d x

y = \frac{2 x}{1 + x ^{2}}, - 4 \leq x \leq 4

\frac{\partial}{\partial y} (\frac{y}{2 x})

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

y = \frac{x ^{6}}{4 - x ^{5}}

What is the integral of xe^{-10x} ?
The integral of xe^{-10x} is 1/100 (-10e^{-10x}x-e^{-10x})+C