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Popular >

integral of xe^2x

Solution

\int x e^{2} x d x

Solution

\frac{e ^{2} x ^{3}}{3} + C

Solution steps

\int x e^{2} x d x

Take the constant out:

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

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

Simplify

xx : x^{2}

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

Apply the Power Rule

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

= e^{2} \frac{x ^{3}}{3}

Multiply fractions:

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

= \frac{e ^{2} x ^{3}}{3}

Add a constant to the solution

= \frac{e ^{2} x ^{3}}{3} + C

Popular Examples

integral of (x^3+5)/(x^2)

\int \frac{x ^{3} + 5}{x ^{2}} d x

tangent of (sqrt(x)+1)/(sqrt(x)+5)tangent of

\frac{x + 1}{x + 5}

derivative of xe^x+x-5e^x-5

\frac{d}{d x} (x e^{x} + x - 5 e^{x} - 5)

derivative of y=xsin(2/x)derivative of

y = x sin (\frac{2}{x})

integral of 4t+1

\int 4 t + 1 d t

Frequently Asked Questions (FAQ)

What is the integral of xe^2x ?
The integral of xe^2x is (e^2x^3)/3+C