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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x^{2} + 4 x - 6 ln ∣ x ∣ + C

Solution steps

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

Expand

\frac{2 x ^{2} + 4 x - 6}{x} : 2 x + 4 - \frac{6}{x}

= \int 2 x + 4 - \frac{6}{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 2 x d x + \int 4 d x - \int \frac{6}{x} d x

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

\int 4 d x = 4 x

\int \frac{6}{x} d x = 6 ln ∣ x ∣

= x^{2} + 4 x - 6 ln ∣ x ∣

Add a constant to the solution

= x^{2} + 4 x - 6 ln ∣ x ∣ + C

\int_{0}^{1} \frac{3 y}{e ^{2 y}} d y

\int ln (2 x + 2) d x

\frac{d}{d x} (x^{2} - 6 x + 7)

\frac{d}{d x} (\frac{x ^{2} - 1}{x ^{2} + 1})

\int 17 tan^{5} (x) sec^{4} (x) d x

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