What is the integral of (9+\sqrt[3]{x})/x ?

The integral of (9+\sqrt[3]{x})/x is 9ln|x|+3\sqrt[3]{x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (9+\sqrt[3]{x})/x

Solution steps

Expand

= \int \frac{9}{x} + \frac{1}{x ^{\frac{2}{3}}} d x

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{9}{x} d x + \int \frac{1}{x ^{\frac{2}{3}}} d x

\int \frac{9}{x} d x = 9 ln ∣ x ∣

\int \frac{1}{x ^{\frac{2}{3}}} d x = 3 x^{\frac{1}{3}}

= 9 ln ∣ x ∣ + 3 x^{\frac{1}{3}}

Apply radical rule:

Add a constant to the solution

\frac{d}{d x} (3 arcsin (x^{4}))

\int \frac{2 x ^{3}}{1 + x ^{4}} d x

\frac{1}{2 + x}

\int 7 x^{\frac{2}{5}} + 6 x^{- \frac{4}{5}} d x

\frac{d}{d x} (- \frac{1}{x ^{5}} - \frac{1}{x ^{3}} + \frac{1}{x})

What is the integral of (9+\sqrt[3]{x})/x ?
The integral of (9+\sqrt[3]{x})/x is 9ln|x|+3\sqrt[3]{x}+C