What is the integral of x^{15}e^{-x^8} ?

The integral of x^{15}e^{-x^8} is 1/8 (-e^{-x^8}x^8-e^{-x^8})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^{15}e^{-x^8}

\int x^{15} e^{- x^{8}} d x

\frac{1}{8} (- e^{- x^{8}} x^{8} - e^{- x^{8}}) + C

Solution steps

\int x^{15} e^{- x^{8}} d x

Apply u-substitution

: \int \frac{e ^{u} u}{8} d u

= \int \frac{e ^{u} u}{8} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int e^{u} u d u

Apply Integration By Parts

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

= \frac{1}{8} (e^{u} u - \int e^{u} d u)

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

= \frac{1}{8} (e^{u} u - e^{u})

Substitute back

u = - x^{8}

= \frac{1}{8} (e^{- x^{8}} (- x^{8}) - e^{- x^{8}})

Simplify

= \frac{1}{8} (- e^{- x^{8}} x^{8} - e^{- x^{8}})

Add a constant to the solution

= \frac{1}{8} (- e^{- x^{8}} x^{8} - e^{- x^{8}}) + C

\int (2 x + 5) (x^{2} + 5 x)^{7} d x

\frac{d y}{d x} = \frac{13 x y}{( ln ( y ) ) ^{10}}

\frac{d h}{d t} = - h, h (0) = 0

y^{^{'}} = \frac{5 y}{x + 3}

x \to - 7 lim (\frac{x ^{2} - 2}{7 - x})

What is the integral of x^{15}e^{-x^8} ?
The integral of x^{15}e^{-x^8} is 1/8 (-e^{-x^8}x^8-e^{-x^8})+C