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Popular >

integral of xe^3x

Solution

\int x e^{3} x d x

Solution

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

Solution steps

\int x e^{3} x d x

Take the constant out:

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

= e^{3} \cdot \int xx d x

Simplify

xx : x^{2}

= e^{3} \cdot \int x^{2} d x

Apply the Power Rule

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

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

Multiply fractions:

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

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

Add a constant to the solution

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

Popular Examples

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derivative of 3x(2x-1)^3 derivative of

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\frac{d}{d x} (1 - sec (x))

integral of (x^{1.5}+9x^{3.5})

\int (x^{1.5} + 9 x^{3.5}) d x

Frequently Asked Questions (FAQ)

What is the integral of xe^3x ?
The integral of xe^3x is (e^3x^3)/3+C