What is the integral of (x^2+x)/(x^3-x^2-2x) ?

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

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integral of (x^2+x)/(x^3-x^2-2x)

\int \frac{x ^{2} + x}{x ^{3} - x ^{2} - 2 x} d x

ln ∣ x - 2 ∣ + C

Solution steps

\int \frac{x ^{2} + x}{x ^{3} - x ^{2} - 2 x} d x

Simplify

\frac{x ^{2} + x}{x ^{3} - x ^{2} - 2 x} : \frac{1}{x - 2}

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x - 2

= ln ∣ x - 2 ∣

Add a constant to the solution

= ln ∣ x - 2 ∣ + C

\int 5 (3 x - 1) 7 d x

ln (3 - x)

\int \frac{1}{1 + 28 x} d x

\frac{d}{d x} (tan (x) \cdot 107.55)

\frac{d}{d x} (\frac{x ^{10}}{20} + \frac{1}{16 x ^{8}})

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