What is the integral of (2x^2-13x+11)/(x-1) ?

The integral of (2x^2-13x+11)/(x-1) is x^2-11x+C

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integral of (2x^2-13x+11)/(x-1)

\int \frac{2 x ^{2} - 13 x + 11}{x - 1} d x

x^{2} - 11 x + C

Solution steps

\int \frac{2 x ^{2} - 13 x + 11}{x - 1} d x

Simplify

\frac{2 x ^{2} - 13 x + 11}{x - 1} : 2 x - 11

= \int 2 x - 11 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 2 x d x - \int 11 d x

\int 2 x d x = x^{2}

\int 11 d x = 11 x

= x^{2} - 11 x

Add a constant to the solution

= x^{2} - 11 x + C

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What is the integral of (2x^2-13x+11)/(x-1) ?
The integral of (2x^2-13x+11)/(x-1) is x^2-11x+C