What is the integral of 7x^{15}e^{-x^8} ?

The integral of 7x^{15}e^{-x^8} is 7/8 (-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 7x^{15}e^{-x^8}

\int 7 x^{15} e^{- x^{8}} d x

\frac{7}{8} (- e^{- x^{8}} x^{8} - e^{- x^{8}}) + C

Solution steps

\int 7 x^{15} e^{- x^{8}} d x

Take the constant out:

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

= 7 \cdot \int x^{15} e^{- x^{8}} d x

Apply u-substitution

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

= 7 \cdot \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

= 7 \cdot \frac{1}{8} \cdot \int e^{u} u d u

Apply Integration By Parts

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

= 7 \cdot \frac{1}{8} (e^{u} u - \int e^{u} d u)

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

= 7 \cdot \frac{1}{8} (e^{u} u - e^{u})

Substitute back

u = - x^{8}

= 7 \cdot \frac{1}{8} (e^{- x^{8}} (- x^{8}) - e^{- x^{8}})

Simplify

7 \cdot \frac{1}{8} (e^{- x^{8}} (- x^{8}) - e^{- x^{8}}) : \frac{7}{8} (- e^{- x^{8}} x^{8} - e^{- x^{8}})

= \frac{7}{8} (- e^{- x^{8}} x^{8} - e^{- x^{8}})

Add a constant to the solution

= \frac{7}{8} (- e^{- x^{8}} x^{8} - e^{- x^{8}}) + C

\int_{1}^{3} \frac{5}{y} d y

x^{2} y^{^{'}} + x (x + 2) y = x

\int \frac{9 sin ( x ) + 2 sec ( x )}{tan ( x )} d x

\frac{d y}{d x} = x + 1

(x + 2 y) d x - x d y = 0

What is the integral of 7x^{15}e^{-x^8} ?
The integral of 7x^{15}e^{-x^8} is 7/8 (-e^{-x^8}x^8-e^{-x^8})+C