What is the integral of xe^{-8x^2} ?

The integral of xe^{-8x^2} is -1/16 e^{-8x^2}+C

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integral of xe^{-8x^2}

\int x e^{- 8 x^{2}} d x

- \frac{1}{16} e^{- 8 x^{2}} + C

Solution steps

\int x e^{- 8 x^{2}} d x

Apply u-substitution

: \int - \frac{e ^{u}}{16} d u

= \int - \frac{e ^{u}}{16} d u

Take the constant out:

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

= - \frac{1}{16} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{16} e^{u}

Substitute back

u = - 8 x^{2}

= - \frac{1}{16} e^{- 8 x^{2}}

Add a constant to the solution

= - \frac{1}{16} e^{- 8 x^{2}} + C

\int 3^{- x} cos (x) d x

\int 1 + \frac{1}{x} d x

\frac{\partial}{\partial y} (5 x^{2} + 8 x y + y^{2})

\frac{d y}{d x} + \frac{5 x ^{2}}{e ^{3 x^{3}}} y = 0

x y^{^{'}} - 2 y = 2 x^{2} + x - 2

What is the integral of xe^{-8x^2} ?
The integral of xe^{-8x^2} is -1/16 e^{-8x^2}+C