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

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

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

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

2 x^{2} - x + C

Solution steps

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

Apply u-substitution

= \int \frac{1}{u} d u

Apply the Power Rule

= 2 u^{\frac{1}{2}}

Substitute back

u = x^{2} - x

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

Apply radical rule:

= 2 x^{2} - x

Add a constant to the solution

= 2 x^{2} - x + C

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