What is the integral of (8x^4-12x^3+6x)/x ?

The integral of (8x^4-12x^3+6x)/x is 2x^4-4x^3+6x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (8x^4-12x^3+6x)/x

\int \frac{8 x ^{4} - 12 x ^{3} + 6 x}{x} d x

2 x^{4} - 4 x^{3} + 6 x + C

Solution steps

\int \frac{8 x ^{4} - 12 x ^{3} + 6 x}{x} d x

Expand

\frac{8 x ^{4} - 12 x ^{3} + 6 x}{x} : \frac{8 x ^{4}}{x} - \frac{12 x ^{3}}{x} + \frac{6 x}{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{8 x ^{4}}{x} d x - \int \frac{12 x ^{3}}{x} d x + \int \frac{6 x}{x} d x

\int \frac{8 x ^{4}}{x} d x = 2 x^{4}

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

\int \frac{6 x}{x} d x = 6 x

= 2 x^{4} - 4 x^{3} + 6 x

Add a constant to the solution

= 2 x^{4} - 4 x^{3} + 6 x + C

\int \frac{x ^{2} + 6 x + 5}{x + 3} d x

\int - 3 e^{- 2 t} d t

\int 1^{2 x} d x

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

\int \frac{5}{4} x d x

What is the integral of (8x^4-12x^3+6x)/x ?
The integral of (8x^4-12x^3+6x)/x is 2x^4-4x^3+6x+C