What is the integral of 6xe^{-x^2} ?

The integral of 6xe^{-x^2} is -3e^{-x^2}+C

Popular >

integral of 6xe^{-x^2}

\int 6 x e^{- x^{2}} d x

- 3 e^{- x^{2}} + C

Solution steps

\int 6 x e^{- x^{2}} d x

Take the constant out:

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

= 6 \cdot \int x e^{- x^{2}} d x

Apply u-substitution

: \int - \frac{e ^{u}}{2} d u

= 6 \cdot \int - \frac{e ^{u}}{2} d u

Take the constant out:

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

= 6 (- \frac{1}{2} \cdot \int e^{u} d u)

Use the common integral:

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

= 6 (- \frac{1}{2} e^{u})

Substitute back

u = - x^{2}

= 6 (- \frac{1}{2} e^{- x^{2}})

Simplify

6 (- \frac{1}{2} e^{- x^{2}}) : - 3 e^{- x^{2}}

= - 3 e^{- x^{2}}

Add a constant to the solution

= - 3 e^{- x^{2}} + C

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

\frac{\partial}{\partial x} (9 x^{2} + y^{2})

n = 1 \sum \infty \frac{n + 5}{5 ^{n}}

\int_{0}^{1} \frac{x ^{6}}{x ^{7} - 1} d x

\int \frac{3}{1 + x ^{2}} d x