What is the integral of (x^2)/(2x^3-1)-2 ?

The integral of (x^2)/(2x^3-1)-2 is 1/6 ln|2x^3-1|-2x+C

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integral of (x^2)/(2x^3-1)-2

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

\frac{1}{6} ln 2 x^{3} - 1 - 2 x + C

Solution steps

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

\int \frac{x ^{2}}{2 x ^{3} - 1} d x = \frac{1}{6} ln 2 x^{3} - 1

\int 2 d x = 2 x

= \frac{1}{6} ln 2 x^{3} - 1 - 2 x

Add a constant to the solution

= \frac{1}{6} ln 2 x^{3} - 1 - 2 x + C

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What is the integral of (x^2)/(2x^3-1)-2 ?
The integral of (x^2)/(2x^3-1)-2 is 1/6 ln|2x^3-1|-2x+C