What is the integral of xe^{-5x^2} ?

The integral of xe^{-5x^2} is -1/10 e^{-5x^2}+C

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integral of xe^{-5x^2}

\int x e^{- 5 x^{2}} d x

- \frac{1}{10} e^{- 5 x^{2}} + C

Solution steps

\int x e^{- 5 x^{2}} d x

Apply u-substitution

: \int - \frac{e ^{u}}{10} d u

= \int - \frac{e ^{u}}{10} d u

Take the constant out:

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

= - \frac{1}{10} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{10} e^{u}

Substitute back

u = - 5 x^{2}

= - \frac{1}{10} e^{- 5 x^{2}}

Add a constant to the solution

= - \frac{1}{10} e^{- 5 x^{2}} + C

\int (2 x + 4) (x^{2} + 4 x + 10)^{4} d x

\int x^{5} x^{3} + 3 d x

\int_{0}^{1} 2 x^{4} e^{- x} d x

y = (x^{2} - 3)^{4}, at x = 2

\frac{d}{d x} (x^{\frac{x}{2}})

What is the integral of xe^{-5x^2} ?
The integral of xe^{-5x^2} is -1/10 e^{-5x^2}+C