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Popular >

integral of e^3x

Solution

\int e^{3} x d x

Solution

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

Solution steps

\int 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 x d x

Apply the Power Rule

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

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

Multiply fractions:

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

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

Add a constant to the solution

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

Popular Examples

integral of 2xe^{-x}

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

area 3(x+1),4(x+1),x=7 area

3 (x + 1), 4 (x + 1), x = 7

integral from 0 to infinity of xe^{-x-y}

\int_{0}^{\infty} x e^{- x - y} d x

integral from 0 to 5 of 1/(x^2+25)

\int_{0}^{5} \frac{1}{x ^{2} + 25} d x

integral of xsin^2(x)cos^2(x)

\int x sin^{2} (x) cos^{2} (x) d x

Frequently Asked Questions (FAQ)

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