What is the integral of x^5e^{2x^3} ?

The integral of x^5e^{2x^3} is 1/12 (e^{2x^3}*2x^3-e^{2x^3})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x^5e^{2x^3}

integral

x^{5} e^{2 x^{3}}

\frac{1}{12} (e^{2 x^{3}} \cdot 2 x^{3} - e^{2 x^{3}}) + C

Solution steps

\int x^{5} e^{2 x^{3}} d x

Apply u-substitution

= \int \frac{e ^{u} u}{12} d u

Take the constant out:

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

= \frac{1}{12} \cdot \int e^{u} u d u

Apply Integration By Parts

= \frac{1}{12} (e^{u} u - \int e^{u} d u)

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

= \frac{1}{12} (e^{u} u - e^{u})

Substitute back

u = 2 x^{3}

= \frac{1}{12} (e^{2 x^{3}} \cdot 2 x^{3} - e^{2 x^{3}})

Add a constant to the solution

= \frac{1}{12} (e^{2 x^{3}} \cdot 2 x^{3} - e^{2 x^{3}}) + C

What is the integral of x^5e^{2x^3} ?
The integral of x^5e^{2x^3} is 1/12 (e^{2x^3}*2x^3-e^{2x^3})+C