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Popular >

integral of e^-x^2

Solution

integral

e^{-} x^{2}

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Multiply fractions:

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

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

Add a constant to the solution

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

Popular Examples

integral of 1/((2x+1)^2+4)

\int \frac{1}{( 2 x + 1 ) ^{2} + 4} d x

integral of ((x-1))/(sqrt(81-4x^2))

\int \frac{( x - 1 )}{81 - 4 x ^{2}} d x

integral of 1/(1+9cos(x))

\int \frac{1}{1 + 9 cos ( x )} d x

integral of (5x-2)/(x(-2))

\int \frac{5 x - 2}{x ( - 2 )} d x

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

\int \frac{5 x ^{2}}{( x - 3 ) ^{3}} d x

Frequently Asked Questions (FAQ)

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