Indefinite Integral Rules
Power, constant multiple and sum rules.
Key idea
Power, constant multiple and sum rules.
In depth
∫xⁿ dx = xⁿ⁺¹/(n + 1) + C for n ≠ −1, ∫1/x dx = ln|x| + C, ∫eˣ dx = eˣ + C, ∫cos x dx = sin x + C. Integrals are linear: split sums and pull out constants.
Worked example
∫(4x³ + 2/x) dx = x⁴ + 2 ln|x| + C.
Formula
Real-world uses
- Finding total distance from speed and total cost from marginal cost formulas
Common mistake
Applying the power rule to 1/x, where it gives division by zero.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Indefinite Integral Rules?
Power, constant multiple and sum rules. It is a topic at the advanced level in Calculus.
What is the formula for Indefinite Integral Rules?
The key formula is ∫xⁿ dx = xⁿ⁺¹/(n+1) + C.
Where is Indefinite Integral Rules used in real life?
Real-world examples: Finding total distance from speed and total cost from marginal cost formulas.
What should I learn before Indefinite Integral Rules?
Make sure you are comfortable with Antiderivatives, the previous topic in Calculus.
What is a common mistake with Indefinite Integral Rules?
Applying the power rule to 1/x, where it gives division by zero.
How can I practise Indefinite Integral Rules?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Indefinite Integral Rules?
Move on to Riemann Sums next.
Related advanced topics in Calculus
- Idea of a Limit – The value a function approaches as the input approaches a point.
- One-Sided Limits – Left and right limits must agree for the limit to exist.
- Limit Laws – Limits of sums, products and quotients are computed from the parts.
- Factoring and Rationalizing Limits – Remove 0/0 indeterminacy with algebra.
- Limits at Infinity – End behaviour of functions.
- Infinite Limits and Asymptotes – Function values grow without bound near a vertical asymptote.