What is the integral of xe^{\sqrt[3]{x}} ?

The integral of xe^{\sqrt[3]{x}} is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of xe^{\sqrt[3]{x}}

Solution steps

Apply u-substitution

= \int 3 e^{u} u^{5} d u

Take the constant out:

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

= 3 \cdot \int e^{u} u^{5} d u

Apply Integration By Parts

= 3 (u^{5} e^{u} - \int 5 u^{4} e^{u} d u)

\int 5 u^{4} e^{u} d u = 5 (u^{4} e^{u} - 4 (u^{3} e^{u} - 3 (u^{2} e^{u} - 2 (e^{u} u - e^{u}))))

= 3 (u^{5} e^{u} - 5 (u^{4} e^{u} - 4 (u^{3} e^{u} - 3 (u^{2} e^{u} - 2 (e^{u} u - e^{u})))))

Substitute back

Simplify

Add a constant to the solution