What is the integral of (4x+2)/(x(x-1)) ?

The integral of (4x+2)/(x(x-1)) is -2ln|x|+6ln|x-1|+C

Popular >

integral of (4x+2)/(x(x-1))

\int \frac{4 x + 2}{x ( x - 1 )} d x

- 2 ln ∣ x ∣ + 6 ln ∣ x - 1 ∣ + C

Solution steps

\int \frac{4 x + 2}{x ( x - 1 )} d x

Take the partial fraction of

\frac{4 x + 2}{x ( x - 1 )} : - \frac{2}{x} + \frac{6}{x - 1}

= \int - \frac{2}{x} + \frac{6}{x - 1} 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{2}{x} d x + \int \frac{6}{x - 1} d x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int \frac{6}{x - 1} d x = 6 ln ∣ x - 1 ∣

= - 2 ln ∣ x ∣ + 6 ln ∣ x - 1 ∣

Add a constant to the solution

= - 2 ln ∣ x ∣ + 6 ln ∣ x - 1 ∣ + C

\int e^{\frac{x}{4}} sin (\frac{x}{8}) cos (\frac{x}{8}) d x

\int (1 + 2 x)^{5} d x

\int 3 x^{2} x^{3} - 1 d x

\int \frac{x}{( 5 x ^{2} - 4 ) ^{4}} d x

\int \frac{sin ^{5} ( x ) - cos ^{2} ( x )}{cos ( x )} d x

What is the integral of (4x+2)/(x(x-1)) ?
The integral of (4x+2)/(x(x-1)) is -2ln|x|+6ln|x-1|+C