What is the integral of (5-10x^2)/(4x^3-6x+15) ?

The integral of (5-10x^2)/(4x^3-6x+15) is -5/6 ln|4x^3-6x+15|+C

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integral of (5-10x^2)/(4x^3-6x+15)

\int \frac{5 - 10 x ^{2}}{4 x ^{3} - 6 x + 15} d x

- \frac{5}{6} ln 4 x^{3} - 6 x + 15 + C

Solution steps

\int \frac{5 - 10 x ^{2}}{4 x ^{3} - 6 x + 15} d x

Apply u-substitution

: \int - \frac{5}{6 u} d u

= \int - \frac{5}{6 u} d u

Take the constant out:

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

= - \frac{5}{6} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{5}{6} ln ∣ u ∣

Substitute back

u = 4 x^{3} - 6 x + 15

= - \frac{5}{6} ln 4 x^{3} - 6 x + 15

Add a constant to the solution

= - \frac{5}{6} ln 4 x^{3} - 6 x + 15 + C

- x^{2} - x + 9, - 0.75 x + 6, x = 0

\frac{\partial}{\partial x} (x^{2} y^{3} z)

\int \frac{1}{x + x ln ( x )} d x

t^{2} y^{^{''}} - 3 t y^{^{'}} + 4 y = t^{\frac{5}{2}}

What is the integral of (5-10x^2)/(4x^3-6x+15) ?
The integral of (5-10x^2)/(4x^3-6x+15) is -5/6 ln|4x^3-6x+15|+C