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

The integral of x^4(e^{x^5}) is 1/5 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 x^4(e^{x^5})

\int x^{4} (e^{x^{5}}) d x

\frac{1}{5} e^{x^{5}} + C

Solution steps

\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

= \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

= \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

= \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

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

Use the common integral:

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

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

Substitute back

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

Simplify

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

= \frac{1}{5} e^{x^{5}}

Add a constant to the solution

= \frac{1}{5} e^{x^{5}} + C

\int (5 x - 4)^{6} d x

\int - \frac{1}{5} x^{- \frac{6}{5}} d x

\int 9 x x^{2} + 4 d x

\int 11 x^{3} d x

\int \frac{sin ( x )}{2 + 5 cos ( x )} d x

What is the integral of x^4(e^{x^5}) ?
The integral of x^4(e^{x^5}) is 1/5 e^{x^5}+C