What is the integral of (x^2-2)/(x^3-6x) ?

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

Popular >

integral of (x^2-2)/(x^3-6x)

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

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

Solution steps

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

Apply u-substitution

: \int \frac{1}{3 u} d u

= \int \frac{1}{3 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} ln ∣ u ∣

Substitute back

u = x^{3} - 6 x

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

Add a constant to the solution

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

\int (4 x - 5) e^{- 3 x} d x

\int \frac{( 2 x ^{2} - 10 x + 14 )}{( x - 3 ) ^{3}} d x

\int 90 x + 4 d x

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

\int 1 - x - 4 x^{3} + 2 x^{5} d x

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