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

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

Popular >

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

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

ln ∣ x + 2 ∣ + ln ∣ x ∣ + C

Solution steps

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

Expand

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

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

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

= 2 ln ∣ x + 2 ∣ - ln ∣ x + 2 ∣ + ln ∣ x ∣

Simplify

= ln ∣ x + 2 ∣ + ln ∣ x ∣

Add a constant to the solution

= ln ∣ x + 2 ∣ + ln ∣ x ∣ + C

\int t^{2} (t^{3} + 4)^{- \frac{1}{2}} d t

\int (4 x^{2} - x) e^{x} d x

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

\int (8 + x^{2})^{- \frac{3}{2}} d x

\int \frac{1}{15 x - 2} d x

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