Question

Evaluate the integral ∫(x² - x)/(18x³ + 3x) dx. (Remember to use absolute values where appropriate. Use c for the constant of integration.)

Answer 1

To solve the integral ∫(x² - x)/(18x³ + 3x) dx, factor the common terms in the denominator and integrate term by term to obtain x²/2 - (1/6)x + c.

Step-by-step explanation:

To evaluate the integral ∫(x² - x)/(18x³ + 3x) dx, we can start by factoring out the constants and the common factor of x in the denominator. This turns our integral into ∫(x - 1/6) dx. Then, we integrate term by term. After integration, we obtain x²/2 - (1/6)x + c, where c represents the constant of integration. It's important to remember that the constant of integration is a key part of the solution in indefinite integrals.