What is the integral of 15xe^{-x^2} ?

The integral of 15xe^{-x^2} is -15/2 e^{-x^2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 15xe^{-x^2}

\int 15 x e^{- x^{2}} d x

- \frac{15}{2} e^{- x^{2}} + C

Solution steps

\int 15 x e^{- x^{2}} d x

Take the constant out:

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

= 15 \cdot \int x e^{- x^{2}} d x

Apply u-substitution

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

= 15 \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

= 15 (- \frac{1}{2} \cdot \int e^{u} d u)

Use the common integral:

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

= 15 (- \frac{1}{2} e^{u})

Substitute back

u = - x^{2}

= 15 (- \frac{1}{2} e^{- x^{2}})

Simplify

15 (- \frac{1}{2} e^{- x^{2}}) : - \frac{15}{2} e^{- x^{2}}

= - \frac{15}{2} e^{- x^{2}}

Add a constant to the solution

= - \frac{15}{2} e^{- x^{2}} + C

\int (x^{2} - 3 x + 2) (cos (x)) d x

\int 2 x - 4 d x

\int \frac{4 sin ( 3 y - 6 )}{cos ( 3 y )} d y

\int (1 - 2 x) (3 + x) d x

sec^{2} (t)

What is the integral of 15xe^{-x^2} ?
The integral of 15xe^{-x^2} is -15/2 e^{-x^2}+C