What is the integral of 4x^5e^{x^6} ?

The integral of 4x^5e^{x^6} is 2/3 e^{x^6}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4x^5e^{x^6}

\int 4 x^{5} e^{x^{6}} d x

\frac{2}{3} e^{x^{6}} + C

Solution steps

\int 4 x^{5} e^{x^{6}} d x

Take the constant out:

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

= 4 \cdot \int x^{5} e^{x^{6}} d x

Apply u-substitution

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

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

= 4 \cdot \frac{1}{5} \cdot \int e^{u^{\frac{6}{5}}} u^{\frac{1}{5}} d u

Apply u-substitution

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

= 4 \cdot \frac{1}{5} \cdot \int \frac{5 e ^{v}}{6} d v

Take the constant out:

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

= 4 \cdot \frac{1}{5} \cdot \frac{5}{6} \cdot \int e^{v} d v

Use the common integral:

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

= 4 \cdot \frac{1}{5} \cdot \frac{5}{6} e^{v}

Substitute back

= 4 \cdot \frac{1}{5} \cdot \frac{5}{6} e^{(x^{5})^{\frac{6}{5}}}

Simplify

4 \cdot \frac{1}{5} \cdot \frac{5}{6} e^{(x^{5})^{\frac{6}{5}}} : \frac{2}{3} e^{x^{6}}

= \frac{2}{3} e^{x^{6}}

Add a constant to the solution

= \frac{2}{3} e^{x^{6}} + C

\frac{\partial}{\partial y} (6 x + 10 y)

\frac{d}{d x} (6 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x))

5 x^{^{''}} + 5 x^{^{'}} + 6 x = 0, x^{^{'}} (0) = 0.45, x (0) = - 0.3

\int \frac{cos ( x )}{x} d x

\frac{\partial}{\partial x} (x z^{2})

What is the integral of 4x^5e^{x^6} ?
The integral of 4x^5e^{x^6} is 2/3 e^{x^6}+C