What is the integral of 6x^5e^{8x^6} ?

The integral of 6x^5e^{8x^6} is 1/8 e^{8x^6}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 6x^5e^{8x^6}

\int 6 x^{5} e^{8 x^{6}} d x

\frac{1}{8} e^{8 x^{6}} + C

Solution steps

\int 6 x^{5} e^{8 x^{6}} d x

Take the constant out:

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

= 6 \cdot \int x^{5} e^{8 x^{6}} d x

Apply u-substitution

: \int \frac{e ^{8 u^{\frac{6}{5}}} u ^{\frac{1}{5}}}{5} d u

= 6 \cdot \int \frac{e ^{8 u^{\frac{6}{5}}} u ^{\frac{1}{5}}}{5} d u

Take the constant out:

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

= 6 \cdot \frac{1}{5} \cdot \int e^{8 u^{\frac{6}{5}}} u^{\frac{1}{5}} d u

Apply u-substitution

: \int \frac{5 e ^{8 v}}{6} d v

= 6 \cdot \frac{1}{5} \cdot \int \frac{5 e ^{8 v}}{6} d v

Take the constant out:

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

= 6 \cdot \frac{1}{5} \cdot \frac{5}{6} \cdot \int e^{8 v} d v

Apply u-substitution

: \int e^{w} \frac{1}{8} d w

= 6 \cdot \frac{1}{5} \cdot \frac{5}{6} \cdot \int e^{w} \frac{1}{8} d w

Take the constant out:

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

= 6 \cdot \frac{1}{5} \cdot \frac{5}{6} \cdot \frac{1}{8} \cdot \int e^{w} d w

Use the common integral:

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

= 6 \cdot \frac{1}{5} \cdot \frac{5}{6} \cdot \frac{1}{8} e^{w}

Substitute back

= 6 \cdot \frac{1}{5} \cdot \frac{5}{6} \cdot \frac{1}{8} e^{8 (x^{5})^{\frac{6}{5}}}

Simplify

6 \cdot \frac{1}{5} \cdot \frac{5}{6} \cdot \frac{1}{8} e^{8 (x^{5})^{\frac{6}{5}}} : \frac{1}{8} e^{8 x^{6}}

= \frac{1}{8} e^{8 x^{6}}

Add a constant to the solution

= \frac{1}{8} e^{8 x^{6}} + C

\frac{3 x ^{2} - 9 x + 13}{3 x + 4}

\int - x^{2} + 4 x - 3 d x

\frac{d}{d x} (9 tan (x))

\frac{\partial}{\partial x} (\frac{10 x}{1 + x ^{2} - y})

\frac{\partial}{\partial y} (\frac{y}{2})

What is the integral of 6x^5e^{8x^6} ?
The integral of 6x^5e^{8x^6} is 1/8 e^{8x^6}+C