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

The integral of ((x-2))/((2x+2)) is 1/2 (x+1-ln(2|x+1|))-ln|2x+2|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((x-2))/((2x+2))

integral

\frac{( x - 2 )}{( 2 x + 2 )}

\frac{1}{2} (x + 1 - ln (2 ∣ x + 1 ∣)) - ln ∣ 2 x + 2 ∣ + C

Solution steps

\int \frac{x - 2}{2 x + 2} d x

Expand

\frac{x - 2}{2 x + 2} : \frac{x}{2 x + 2} - \frac{2}{2 x + 2}

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{x}{2 x + 2} d x - \int \frac{2}{2 x + 2} d x

\int \frac{x}{2 x + 2} d x = \frac{1}{2} (x + 1 - ln (2 ∣ x + 1 ∣))

\int \frac{2}{2 x + 2} d x = ln ∣ 2 x + 2 ∣

= \frac{1}{2} (x + 1 - ln (2 ∣ x + 1 ∣)) - ln ∣ 2 x + 2 ∣

Add a constant to the solution

= \frac{1}{2} (x + 1 - ln (2 ∣ x + 1 ∣)) - ln ∣ 2 x + 2 ∣ + C

\frac{x ^{3}}{e ^{x}}

sin^{2} (x) cos^{4} (x)

\frac{( x ^{2} + 1 )}{( 3 x - x ^{2} )}

\frac{- 1}{y}

f (x) = \frac{1}{( 1 - x ) ^{\frac{1}{2}}}

What is the integral of ((x-2))/((2x+2)) ?
The integral of ((x-2))/((2x+2)) is 1/2 (x+1-ln(2|x+1|))-ln|2x+2|+C