What is the integral of (4x^2-2)/(x^3-x) ?

The integral of (4x^2-2)/(x^3-x) is ln|x^2-1|+2ln(x)+C

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integral of (4x^2-2)/(x^3-x)

\int \frac{4 x ^{2} - 2}{x ^{3} - x} d x

ln x^{2} - 1 + 2 ln (x) + C

Solution steps

\int \frac{4 x ^{2} - 2}{x ^{3} - x} d x

Apply u-substitution

: \int \frac{2 u - 1}{u ( u - 1 )} d u

= \int \frac{2 u - 1}{u ( u - 1 )} d u

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

= ln x^{2} (x^{2} - 1)

Simplify

ln x^{2} (x^{2} - 1) : ln x^{2} - 1 + 2 ln (x)

= ln x^{2} - 1 + 2 ln (x)

Add a constant to the solution

= ln x^{2} - 1 + 2 ln (x) + C

\int x^{\frac{1}{3}} + 3 d x

\frac{\partial}{\partial x} (x sin (y) + z e^{x})

\int (6 x - 7) d x

f (x) = \frac{1 - 2 ln ( x )}{x ^{3}}

sin (3 x^{2})

What is the integral of (4x^2-2)/(x^3-x) ?
The integral of (4x^2-2)/(x^3-x) is ln|x^2-1|+2ln(x)+C