Evaluate an indefinite integral by dividing the numerator by the denominator and applying the power rule.

Vault Of Euclid

Integrating a Rational Function by Splitting the Numerator

Antiderivatives warmup

Evaluate \( \int \frac{x^3-1}{x^3} \, dx \).

The solution and a full step-by-step explanation are here. Sign in to read them.

What you need first

Basic algebra with exponents
The power rule for integration
The concept of an indefinite integral and the constant of integration

What this problem tests

Tests the student's ability to recognize when to simplify an integrand algebraically before attempting to integrate, and their proficiency with negative exponents in the power rule.

This is a standard introductory calculus problem demonstrating how algebraic simplification can turn a seemingly complex integral into basic power rule applications.

Integrating a Rational Function by Splitting the Numerator

What you need first

What this problem tests

More on Antiderivatives