What is the integral of x^{14}e^{x^{15}} ?

The integral of x^{14}e^{x^{15}} is 1/15 e^{x^{15}}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^{14}e^{x^{15}}

\int x^{14} e^{x^{15}} d x

\frac{1}{15} e^{x^{15}} + C

Solution steps

\int x^{14} e^{x^{15}} d x

Apply u-substitution

: \int \frac{e ^{u^{\frac{15}{14}}} u ^{\frac{1}{14}}}{14} d u

= \int \frac{e ^{u^{\frac{15}{14}}} u ^{\frac{1}{14}}}{14} d u

Take the constant out:

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

= \frac{1}{14} \cdot \int e^{u^{\frac{15}{14}}} u^{\frac{1}{14}} d u

Apply u-substitution

: \int \frac{14 e ^{v}}{15} d v

= \frac{1}{14} \cdot \int \frac{14 e ^{v}}{15} d v

Take the constant out:

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

= \frac{1}{14} \cdot \frac{14}{15} \cdot \int e^{v} d v

Use the common integral:

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

= \frac{1}{14} \cdot \frac{14}{15} e^{v}

Substitute back

= \frac{1}{14} \cdot \frac{14}{15} e^{(x^{14})^{\frac{15}{14}}}

Simplify

\frac{1}{14} \cdot \frac{14}{15} e^{(x^{14})^{\frac{15}{14}}} : \frac{1}{15} e^{x^{15}}

= \frac{1}{15} e^{x^{15}}

Add a constant to the solution

= \frac{1}{15} e^{x^{15}} + C

\int \frac{3}{4} d x

\int 11 arctan (x) d x

y = - (x - 2)^{2} + 16

\int \frac{8 x + 28}{x ^{2} + 8 x + 12} d x

\int \frac{x + 7}{2 x ^{3} - 8 x} d x

What is the integral of x^{14}e^{x^{15}} ?
The integral of x^{14}e^{x^{15}} is 1/15 e^{x^{15}}+C