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

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

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

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

Solution steps

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

Apply u-substitution

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

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

Apply u-substitution

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

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

Apply u-substitution

: \int e^{w} \frac{1}{6} d w

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

Substitute back

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

Simplify

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

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

Add a constant to the solution

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

\int 6 x + 7 d x

\int e^{3 x} + 2 d x

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

\int_{1}^{7} \frac{5}{x ^{2}} d x

\int x ln (2) + \frac{3}{2 x} d x

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