What is the integral of 1/((x+1)x) ?

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

Popular >

integral of 1/((x+1)x)

\int \frac{1}{( x + 1 ) x} d x

- ln ∣ x + 1 ∣ + ln ∣ x ∣ + C

Solution steps

\int \frac{1}{( x + 1 ) x} d x

Take the partial fraction of

\frac{1}{( x + 1 ) x} : - \frac{1}{x + 1} + \frac{1}{x}

= \int - \frac{1}{x + 1} + \frac{1}{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 \frac{1}{x + 1} d x + \int \frac{1}{x} d x

\int \frac{1}{x + 1} d x = ln ∣ x + 1 ∣

\int \frac{1}{x} d x = ln ∣ x ∣

= - ln ∣ x + 1 ∣ + ln ∣ x ∣

Add a constant to the solution

= - ln ∣ x + 1 ∣ + ln ∣ x ∣ + C

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

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

\int cos (x) sin (x) + 3 d x

\int \frac{sec ^{2} ( w )}{1 + tan ^{2} ( w )} d w

\int (2 x^{2} y) d y

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