Practice Flashcards
Flip to reveal answersHow do you integrate (ax + b)ⁿ?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 9 Flashcards — Reverse chain rule
Sign up free to track progress and get spaced-repetition review schedules.
Question
How do you integrate (ax + b)ⁿ?
Answer
(ax+b)ⁿ⁺¹/[a(n+1)] + C — integrate as usual, then divide by the inner coefficient a.
Question
∫sin(ax + b) dx = ?
Answer
−cos(ax+b)/a + C.
Question
∫cos(ax + b) dx = ?
Answer
sin(ax+b)/a + C.
Question
∫e^(ax + b) dx = ?
Answer
e^(ax+b)/a + C.
Question
∫1/(ax + b) dx = ?
Answer
(1/a)ln|ax+b| + C.
Question
Why divide by the inner coefficient?
Answer
To undo the ×a that the chain rule would introduce when differentiating.
Question
State the f'/f rule.
Answer
∫ f'(x)/f(x) dx = ln|f(x)| + C (numerator is the derivative of the denominator).
Question
∫2x(x² + 1)³ dx = ?
Answer
(x²+1)⁴/4 + C (reverse chain: 2x is the inner derivative).
Question
How do you check a reverse-chain integral?
Answer
Differentiate your answer — it should give back the integrand.
Read the notes
Full study notes for Reverse chain rule
Topic 5.10 hub
Integration by substitution
More from Topic 5.10
All flashcards in this topic
Math AA SL exam skills
Paper structures & tips
Track your progress with spaced repetition
Sign up free — Aimnova tells you exactly which cards to review and when, so you remember everything before your IB exam.
Start Free