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Popular >

integral of xex

Solution

\int x e x d x

Solution

\frac{e x ^{3}}{3} + C

Solution steps

\int x e x d x

Take the constant out:

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

= e \cdot \int xx d x

Simplify

xx : x^{2}

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

Apply the Power Rule

: \frac{x ^{3}}{3}

= e \frac{x ^{3}}{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{e x ^{3}}{3}

Add a constant to the solution

= \frac{e x ^{3}}{3} + C

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integral from 0 to t of t^2e^{-3t}

\int_{0}^{t} t^{2} e^{- 3 t} d t

Frequently Asked Questions (FAQ)

What is the integral of xex ?
The integral of xex is (ex^3)/3+C