What is the integral of (6x^3-5)/x ?

The integral of (6x^3-5)/x is 2x^3-5ln|x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (6x^3-5)/x

\int \frac{6 x ^{3} - 5}{x} d x

2 x^{3} - 5 ln ∣ x ∣ + C

Solution steps

\int \frac{6 x ^{3} - 5}{x} d x

Expand

\frac{6 x ^{3} - 5}{x} : 6 x^{2} - \frac{5}{x}

= \int 6 x^{2} - \frac{5}{x} 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 6 x^{2} d x - \int \frac{5}{x} d x

\int 6 x^{2} d x = 2 x^{3}

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= 2 x^{3} - 5 ln ∣ x ∣

Add a constant to the solution

= 2 x^{3} - 5 ln ∣ x ∣ + C

x \to 1 lim (\frac{x ^{15} - 1}{x ^{5} - 1})

(\frac{1}{1 - cos ( x )})^{^{'}}

(\frac{1}{x ^{2} + 1})^{^{'}}

\frac{\partial}{\partial x} (sin (2 y x))

What is the integral of (6x^3-5)/x ?
The integral of (6x^3-5)/x is 2x^3-5ln|x|+C