What is the integral of 9x^8e^{4x^9} ?

The integral of 9x^8e^{4x^9} is 1/4 e^{4x^9}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 9x^8e^{4x^9}

\int 9 x^{8} e^{4 x^{9}} d x

\frac{1}{4} e^{4 x^{9}} + C

Solution steps

\int 9 x^{8} e^{4 x^{9}} d x

Take the constant out:

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

= 9 \cdot \int x^{8} e^{4 x^{9}} d x

Apply u-substitution

: \int \frac{e ^{4 u^{\frac{9}{8}}} u ^{\frac{1}{8}}}{8} d u

= 9 \cdot \int \frac{e ^{4 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

= 9 \cdot \frac{1}{8} \cdot \int e^{4 u^{\frac{9}{8}}} u^{\frac{1}{8}} d u

Apply u-substitution

: \int \frac{8 e ^{4 v}}{9} d v

= 9 \cdot \frac{1}{8} \cdot \int \frac{8 e ^{4 v}}{9} d v

Take the constant out:

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

= 9 \cdot \frac{1}{8} \cdot \frac{8}{9} \cdot \int e^{4 v} d v

Apply u-substitution

: \int e^{w} \frac{1}{4} d w

= 9 \cdot \frac{1}{8} \cdot \frac{8}{9} \cdot \int e^{w} \frac{1}{4} d w

Take the constant out:

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

= 9 \cdot \frac{1}{8} \cdot \frac{8}{9} \cdot \frac{1}{4} \cdot \int e^{w} d w

Use the common integral:

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

= 9 \cdot \frac{1}{8} \cdot \frac{8}{9} \cdot \frac{1}{4} e^{w}

Substitute back

= 9 \cdot \frac{1}{8} \cdot \frac{8}{9} \cdot \frac{1}{4} e^{4 (x^{8})^{\frac{9}{8}}}

Simplify

9 \cdot \frac{1}{8} \cdot \frac{8}{9} \cdot \frac{1}{4} e^{4 (x^{8})^{\frac{9}{8}}} : \frac{1}{4} e^{4 x^{9}}

= \frac{1}{4} e^{4 x^{9}}

Add a constant to the solution

= \frac{1}{4} e^{4 x^{9}} + C

\frac{\partial}{\partial x} (x^{2} ln (3 y - 5))

\int 16 tan^{4} (x se) c^{6} x d x

\int x (x^{\frac{3}{2}} - 4)^{3} d x

\int sin^{3} (x co) s^{18} x

y^{^{''}} - 3 y^{^{'}} + 2.25 y = 27 (x^{2} - x)

What is the integral of 9x^8e^{4x^9} ?
The integral of 9x^8e^{4x^9} is 1/4 e^{4x^9}+C