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Popular >

integral of e^2x

Solution

\int e^{2} x d x

Solution

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

Solution steps

\int 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 x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

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

Multiply fractions:

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

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

Add a constant to the solution

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

Popular Examples

(e^x+e^{-x})y^'=y^2

(e^{x} + e^{- x}) y^{^{'}} = y^{2}

integral of x^{-4}+2x+3

\int x^{- 4} + 2 x + 3 d x

limit as x approaches 0 of (21^x-1)/x

x \to 0 lim (\frac{2 1 ^{x} - 1}{x})

integral of 1/(2sqrt(x)(1+x))

\int \frac{1}{2 x ( 1 + x )} d x

y^'= 2/3 xsqrt(1-9y^2)

y^{^{'}} = \frac{2}{3} x 1 - 9 y^{2}

Frequently Asked Questions (FAQ)

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