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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (6x+2)/(3x^2+2x)

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

ln 3 x^{2} + 2 x + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = 3 x^{2} + 2 x

= ln 3 x^{2} + 2 x

Add a constant to the solution

= ln 3 x^{2} + 2 x + C

\int_{0}^{1} \frac{1}{3 - x ^{2}} d x

\int \frac{x ^{6}}{( 4 - x ^{7} ) ^{2}} d x

\frac{d}{d x} (7 sec (x) tan (x))

\int_{2}^{4} e^{3 x - y} d y

\frac{d}{d x} ((3^{\frac{2}{3}} - x^{\frac{2}{3}})^{\frac{3}{2}})

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