What is the integral of x^8e^{x^9} ?

The integral of x^8e^{x^9} is 1/9 e^{x^9}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^8e^{x^9}

\int x^{8} e^{x^{9}} d x

\frac{1}{9} e^{x^{9}} + C

Solution steps

\int x^{8} e^{x^{9}} d x

Apply u-substitution

: \int \frac{e ^{u^{\frac{9}{8}}} u ^{\frac{1}{8}}}{8} d u

= \int \frac{e ^{u^{\frac{9}{8}}} u ^{\frac{1}{8}}}{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^{\frac{9}{8}}} u^{\frac{1}{8}} d u

Apply u-substitution

: \int \frac{8 e ^{v}}{9} d v

= \frac{1}{8} \cdot \int \frac{8 e ^{v}}{9} d v

Take the constant out:

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

= \frac{1}{8} \cdot \frac{8}{9} \cdot \int e^{v} d v

Use the common integral:

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

= \frac{1}{8} \cdot \frac{8}{9} e^{v}

Substitute back

= \frac{1}{8} \cdot \frac{8}{9} e^{(x^{8})^{\frac{9}{8}}}

Simplify

\frac{1}{8} \cdot \frac{8}{9} e^{(x^{8})^{\frac{9}{8}}} : \frac{1}{9} e^{x^{9}}

= \frac{1}{9} e^{x^{9}}

Add a constant to the solution

= \frac{1}{9} e^{x^{9}} + C

\frac{d}{d x} (\frac{x ^{2}}{4 ^{x}})

\frac{d x}{d y} + 3 x y^{3} = 0

3 y^{2} - 2 x^{2} = 6 - 2 x y, (3, 2)

y = x^{2} - 11, y = 10 x

What is the integral of x^8e^{x^9} ?
The integral of x^8e^{x^9} is 1/9 e^{x^9}+C