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

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

Popular >

integral of-xe^{-(x^2)/2}

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int - e^{u} d u

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

Take the constant out:

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

= - (- \int e^{u} d u)

Use the common integral:

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

= - (- e^{u})

Substitute back

u = - \frac{x ^{2}}{2}

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

Simplify

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

Add a constant to the solution

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

\int (cot (x))^{4} d x

\int \frac{x ^{2}}{4 x ^{2} - 9} d x

\int x (π - x) sin (n x) d x

\int \frac{x ^{3} + 3 x ^{2} + 2 x + 5}{x + 2} d x

\int sin (\frac{π}{6} x) d x

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