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

The integral of x^2+x+2/(x-1) is (x^3)/3+(x^2)/2+2ln|x-1|+C

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

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

\frac{x ^{3}}{3} + \frac{x ^{2}}{2} + 2 ln ∣ x - 1 ∣ + C

Solution steps

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

\int x^{2} d x = \frac{x ^{3}}{3}

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

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

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + 2 ln ∣ x - 1 ∣

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + 2 ln ∣ x - 1 ∣ + C

y = \frac{x ^{2}}{x - 4}

f (x) = 1 + x^{2}

\frac{d y}{d x} = x - 5

\int 3 3 x + 1 d x

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

What is the integral of x^2+x+2/(x-1) ?
The integral of x^2+x+2/(x-1) is (x^3)/3+(x^2)/2+2ln|x-1|+C