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Popular >

integral of e^2x^2

Solution

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

Solution

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

Solution steps

\int e^{2} x^{2} 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^{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 sqrt((5-2x)/(4+3x))

\int \frac{5 - 2 x}{4 + 3 x} d x

integral of-2/(1+x^2)

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

integral of sqrt(cos^2(x)+sin^2(x))

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

integral of 2/(200+x)

\int \frac{2}{200 + x} d x

integral of (x^2*arctan(x))/(1+x^2)

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

Frequently Asked Questions (FAQ)

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