What is the integral of (1+\sqrt[3]{x})/(sqrt(x)) ?

The integral of (1+\sqrt[3]{x})/(sqrt(x)) is 2sqrt(x)+6/5 x^{5/6}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (1+\sqrt[3]{x})/(sqrt(x))

2 x + \frac{6}{5} x^{\frac{5}{6}} + C

Solution steps

Expand

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

\int \frac{1}{x} d x = 2 x

= 2 x + \frac{6}{5} x^{\frac{5}{6}}

Add a constant to the solution

= 2 x + \frac{6}{5} x^{\frac{5}{6}} + C

What is the integral of (1+\sqrt[3]{x})/(sqrt(x)) ?
The integral of (1+\sqrt[3]{x})/(sqrt(x)) is 2sqrt(x)+6/5 x^{5/6}+C