What is the integral of (6x^2-12)/(x^3-6x+1) ?

The integral of (6x^2-12)/(x^3-6x+1) is 2ln|x^3-6x+1|+C

Popular >

integral of (6x^2-12)/(x^3-6x+1)

\int \frac{6 x ^{2} - 12}{x ^{3} - 6 x + 1} d x

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

Solution steps

\int \frac{6 x ^{2} - 12}{x ^{3} - 6 x + 1} d x

Apply u-substitution

: \int \frac{2}{u} d u

= \int \frac{2}{u} d u

Take the constant out:

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

= 2 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 ln ∣ u ∣

Substitute back

u = x^{3} - 6 x + 1

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

Add a constant to the solution

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

\int e^{x} - 9 d x

\int \frac{cos ( 4 x )}{sin ( 2 x )} d x

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

\int \frac{x ^{2} + 9 x + 2}{( x - 1 ) ( x + 1 ) ( x + 2 )} d x

\int sin (0.01 t) + t^{3} d t

What is the integral of (6x^2-12)/(x^3-6x+1) ?
The integral of (6x^2-12)/(x^3-6x+1) is 2ln|x^3-6x+1|+C