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

The integral of-4x^4e^{x^5} is -4/5 e^{x^5}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

- \frac{4}{5} e^{x^{5}} + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int \frac{e ^{u^{\frac{5}{4}}} u ^{\frac{1}{4}}}{4} d u

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

Take the constant out:

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

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

Apply u-substitution

: \int \frac{4 e ^{v}}{5} d v

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

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

Simplify

- 4 \cdot \frac{1}{4} \cdot \frac{4}{5} e^{(x^{4})^{\frac{5}{4}}} : - \frac{4}{5} e^{x^{5}}

= - \frac{4}{5} e^{x^{5}}

Add a constant to the solution

= - \frac{4}{5} e^{x^{5}} + C

\int 1 + (\frac{x ^{2}}{2} - \frac{1}{2 x ^{2}})^{2} d x

\int (x sin (x))^{2} d x

\int \frac{2 x + 3}{9 - 8 x - x ^{2}} d x

\int 6 z 4 + z^{2} d z

\int \frac{x ^{2} + 1}{x ^{3}} d x

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