What is the integral of xe^{-2x^2} ?

The integral of xe^{-2x^2} is -1/4 e^{-2x^2}+C

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integral of xe^{-2x^2}

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

- \frac{1}{4} e^{- 2 x^{2}} + C

Solution steps

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

Apply u-substitution

: \int - \frac{e ^{u}}{4} d u

= \int - \frac{e ^{u}}{4} d u

Take the constant out:

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

= - \frac{1}{4} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= - \frac{1}{4} e^{u}

Substitute back

u = - 2 x^{2}

= - \frac{1}{4} e^{- 2 x^{2}}

Add a constant to the solution

= - \frac{1}{4} e^{- 2 x^{2}} + C

\int arctan (x) + C d x

\int 36 arctan (x) d x

y^{^{'}} + 2 x y + x y^{4} = 0

\frac{8}{3 x + 2}, 5

\int \frac{1}{t ^{2} - 4 t + 20} d t

What is the integral of xe^{-2x^2} ?
The integral of xe^{-2x^2} is -1/4 e^{-2x^2}+C