What is the integral of (12x^3-6x^2+4/x) ?

The integral of (12x^3-6x^2+4/x) is 3x^4-2x^3+4ln|x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (12x^3-6x^2+4/x)

\int (12 x^{3} - 6 x^{2} + \frac{4}{x}) d x

3 x^{4} - 2 x^{3} + 4 ln ∣ x ∣ + C

Solution steps

\int 12 x^{3} - 6 x^{2} + \frac{4}{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 12 x^{3} d x - \int 6 x^{2} d x + \int \frac{4}{x} d x

\int 12 x^{3} d x = 3 x^{4}

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

\int \frac{4}{x} d x = 4 ln ∣ x ∣

= 3 x^{4} - 2 x^{3} + 4 ln ∣ x ∣

Add a constant to the solution

= 3 x^{4} - 2 x^{3} + 4 ln ∣ x ∣ + C

\int x (1 - x^{2}) d x

\int t e^{9 t} d t

\int e^{x} - 3 cos (x) d x

\int sin^{3} (6 x) cos (6 x) d x

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

What is the integral of (12x^3-6x^2+4/x) ?
The integral of (12x^3-6x^2+4/x) is 3x^4-2x^3+4ln|x|+C