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

The integral of (x^4e^{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^4e^{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 a sin (b x) d x

\int \frac{7 + 8 x}{1 + x ^{2}} d x

\int \frac{1}{x ( 3 + ln ( x ) )} d x

\int \frac{16 x ^{3} + 12 x ^{2} + 5 x + 8}{4} d x

\int \frac{- 4 x - 2}{( x - 3 ) ^{2}} d x

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