What is the integral of (6x-11)/((x-1)^2) ?

The integral of (6x-11)/((x-1)^2) is 6ln|x-1|+5/(x-1)+C

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integral of (6x-11)/((x-1)^2)

\int \frac{6 x - 11}{( x - 1 ) ^{2}} d x

6 ln ∣ x - 1 ∣ + \frac{5}{x - 1} + C

Solution steps

\int \frac{6 x - 11}{( x - 1 ) ^{2}} d x

Expand

\frac{6 x - 11}{( x - 1 ) ^{2}} : \frac{6 x}{( x - 1 ) ^{2}} - \frac{11}{( x - 1 ) ^{2}}

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{6 x}{( x - 1 ) ^{2}} d x - \int \frac{11}{( x - 1 ) ^{2}} d x

\int \frac{6 x}{( x - 1 ) ^{2}} d x = 6 (ln ∣ x - 1 ∣ - \frac{1}{x - 1})

\int \frac{11}{( x - 1 ) ^{2}} d x = - \frac{11}{x - 1}

= 6 (ln ∣ x - 1 ∣ - \frac{1}{x - 1}) - (- \frac{11}{x - 1})

Simplify

6 (ln ∣ x - 1 ∣ - \frac{1}{x - 1}) - (- \frac{11}{x - 1}) : 6 ln ∣ x - 1 ∣ + \frac{5}{x - 1}

= 6 ln ∣ x - 1 ∣ + \frac{5}{x - 1}

Add a constant to the solution

= 6 ln ∣ x - 1 ∣ + \frac{5}{x - 1} + C

\frac{6}{( 6 - x ^{6} ) ^{\frac{3}{2}}}

\int \frac{x ^{3}}{( x ^{2} + 4 ) ^{\frac{3}{2}}} d x

\frac{6}{( s + 3 ) ^{2}}

\int (1 - 3 x)^{\frac{1}{2}} d x

x^{2}

What is the integral of (6x-11)/((x-1)^2) ?
The integral of (6x-11)/((x-1)^2) is 6ln|x-1|+5/(x-1)+C