Next: Definite Integration
OpenStandard integrals, substitution, integration by parts, partial fractions and special forms.
Standard integrals, substitution, integration by parts, partial fractions and special forms.
Maths · Class 12 · Integral Calculus
Indefinite Integration for JEE
Everything you need for this topic on one page: the ideas, the formulas, the traps, and free lectures that explain it well.
Last updated: 26 October 2026
Key ideas
Indefinite Integration: what you must understand
- Integration is the reverse of differentiation
- Choose substitution when the derivative of a part is present
- By parts: ILATE order to pick u
- Partial fractions for rational functions
Formula sheet
Must-know formulas for Indefinite Integration
- ∫xⁿ dx = xⁿ⁺¹/(n+1) + C
- ∫u v dx = u∫v dx − ∫(u′∫v dx) dx
- ∫dx/(x² + a²) = (1/a) tan⁻¹(x/a) + C
- ∫eˣ[f(x) + f′(x)] dx = eˣf(x) + C
Print
One-page formula sheet
Printable Indefinite Integration formula sheet: formulas, key ideas and traps on one page. Save it as a PDF for offline revision.
Avoid
Common mistakes students make
- Forgetting + C
- Wrong partial fraction setup for repeated factors
- Choosing u badly in by parts
For the exam
How this topic is asked in JEE
Appears frequently. Practise speed. Integration feeds definite integration and differential equations.
Prerequisites: Continuity and Differentiability.
NCERT map
Where Indefinite Integration is in NCERT
Chapter names follow the current rationalised NCERT textbooks. Read these sections before solving PYQs.
| Class | Book | Chapter | Sections JEE asks from |
|---|---|---|---|
| Class 12 | Mathematics Part II | Integrals | Integration by Substitution; Integration by Partial Fractions; Integration by Parts; Integrals of Some Particular Functions; Some Properties of Indefinite Integrals |
JEE Advanced level
A JEE Advanced-level example on Indefinite Integration
Question. Evaluate ∫ (x² + 1) / (x⁴ + 1) dx
Show solution
- Divide both numerator and denominator by x² to get ∫ (1 + 1/x²) / (x² + 1/x²) dx
- Rewrite the denominator: x² + 1/x² = (x − 1/x)² + 2
- Substitute t = x − 1/x, so dt = (1 + 1/x²) dx
- The integral becomes ∫ dt / (t² + 2) which is a standard form
- Apply the formula ∫ dt/(t² + a²) = (1/a) tan⁻¹(t/a) + C with a = √2
- Substitute back t = x − 1/x to get the final answer
Answer: (1/√2) tan⁻¹[(x² − 1)/(√2 · x)] + C
This example was solved twice independently and both solutions agree.
Free lectures
Best free lectures for Indefinite Integration
Full-chapter free lectures picked from YouTube search results by views, from established JEE channels (mostly in Hinglish). Use the subtopic list to jump straight to the part you need (timestamps come from each video's own chapter list). Watch one, then solve PYQs the same day.
- INDEFINITE INTEGRATION in One Shot: All Concepts & PYQs Covered | JEE Main & Advanced — JEE Wallah, 5:19:25
Jump to a subtopic (16)
- 00:00 Introduction
- 02:58 Topics to be covered
- 04:09 Integration as reserve of differentiation
- 07:42 Basic formulas in integration
- 42:18 Integration by substitution
- 1:12:36 6 important formulas
- 1:18:18 General trigo substitution
- 1:48:06 6 important integrals and methods to solve them
- 3:03:32 Integration of parts
- 3:43:49 Two important applications of parts
- 4:06:12 3 important formula
- 4:19:42 Integrals by negative powers
- 4:37:11 Integration by partial fraction
- 5:01:59 Reduction integrals
- 5:16:45 Homework
- 5:18:25 Thank You Bacchon
- JEE Brief: Indefinite Integration One Shot MATHS Class 12 JEE Main and Advanced — Vora Classes, 4:37:42
Practise
Where to practise for free
- 1 JEE Main 2026 PYQs on Indefinite Integration, with solutions.
- Read the chapter in NCERT textbooks (official, free), then solve its NCERT Exemplar (official, free) questions.
- Chapter-wise past questions: JEE Main and Advanced PYQs and question bank.
- Timed practice tests: NTA Abhyas practice tests (official, free) and our free mock tests.
- See it move: interactive simulation.
FAQs
Frequently asked questions
Is Indefinite Integration important for JEE Main 2027?
Appears frequently. It is part of the official 'Integral Calculus' unit in the JEE Main 2027 syllabus.
What are the most important formulas in Indefinite Integration?
∫xⁿ dx = xⁿ⁺¹/(n+1) + C; ∫u v dx = u∫v dx − ∫(u′∫v dx) dx; ∫dx/(x² + a²) = (1/a) tan⁻¹(x/a) + C.
How should I study Indefinite Integration for JEE?
Understand the key ideas from NCERT or one full lecture, learn the formula sheet, then solve 25–30 past JEE questions on the topic. Practise speed. Integration feeds definite integration and differential equations.