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Popular >

integral of 2xe^2x

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Simplify

xx : x^{2}

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

Apply the Power Rule

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

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

Multiply fractions:

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

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

Add a constant to the solution

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

Popular Examples

limit as x approaches 1 of sqrt(5-x)

x \to 1 lim (5 - x)

integral from 6 to 8 of (100)/((x-6)^3)

\int_{6}^{8} \frac{100}{( x - 6 ) ^{3}} d x

derivative of 5/((x+1^2))

\frac{d}{d x} (\frac{5}{( x + 1 ) ^{2}})

integral of (e^{5x}+e^{-5x})^2

\int (e^{5 x} + e^{- 5 x})^{2} d x

integral of (2^{x+1}-3^{x+1})/(2^{x+1)}

\int \frac{2 ^{x + 1} - 3 ^{x + 1}}{2 ^{x + 1}} d x

Frequently Asked Questions (FAQ)

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