What is the integral of e^{-2}(x)^2 ?

The integral of e^{-2}(x)^2 is (x^3)/(3e^2)+C

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

integral

e^{- 2} (x)^{2}

\frac{x ^{3}}{3 e ^{2}} + 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 exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{2}} \cdot \int x^{2} d x

Apply the Power Rule

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

= \frac{1}{e ^{2}} \cdot \frac{x ^{3}}{3}

Simplify

\frac{1}{e ^{2}} \cdot \frac{x ^{3}}{3} : \frac{x ^{3}}{3 e ^{2}}

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

Add a constant to the solution

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

\frac{2 x}{3}

\frac{( t + 1 )}{t}

(e^{- 2} x) sinh^{2} (x)

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

sin^{3} (2 x + 5)

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