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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{1}{x ^{14}})

(5 - e^{- 4 x})^{4}

\int_{1}^{\infty} \frac{4}{x ^{2}} d x

\int 2^{x} + 8 sinh (x) d x

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