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Popular Calculus >

integral of xe^{-1}

Solution

\int x e^{- 1} d x

Solution

\frac{x ^{2}}{2 e} + C

Solution steps

\int x e^{- 1} d x

Take the constant out:

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

= e^{- 1} \cdot \int x d x

Apply exponent rule:

a^{- 1} = \frac{1}{a}

= \frac{1}{e} \cdot \int x d x

Apply the Power Rule

= \frac{1}{e} \cdot \frac{x ^{2}}{2}

Simplify

\frac{1}{e} \cdot \frac{x ^{2}}{2} : \frac{x ^{2}}{2 e}

= \frac{x ^{2}}{2 e}

Add a constant to the solution

= \frac{x ^{2}}{2 e} + C

Graph

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

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\frac{\partial}{\partial x} (x^{8} + 2^{y} + x^{y})

y^{^{'}} = \frac{x}{y ^{2}}

t(dy)/(dt)+2y=t^2

t \frac{d y}{d t} + 2 y = t^{2}

Frequently Asked Questions (FAQ)

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