Class 12 Maths | Integration of Important Functions | Frequently Asked Board Exam Integrals

Hello baccho,
Welcome back to the Class 12 Integration series! ✨
In this video, we revise and explain the *integration of some very important functions*
that are repeatedly asked in CBSE Board Exams, NCERT examples, and sample papers.

These integrals form the backbone of almost every long-answer calculus question.

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📘 *Important Functions Covered in This Video:*

✔️ Polynomial Functions
∫ xⁿ dx (n ≠ −1)

✔️ Rational Functions
∫ 1/x dx
∫ 1/(ax + b) dx

✔️ Exponential Functions
∫ eˣ dx
∫ aˣ dx

✔️ Trigonometric Functions
∫ sin x dx
∫ cos x dx
∫ sec²x dx
∫ cosec²x dx
∫ sec x tan x dx
∫ cosec x cot x dx

✔️ Inverse Trigonometric Forms
∫ 1/√(a² − x²) dx
∫ 1/(a² + x²) dx

✔️ Logarithmic Results & Constant of Integration

✔️ NCERT-based solved examples
✔️ Board-level important problems

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💡 *What You’ll Learn:*
• How to quickly identify which standard result to use
• How to avoid sign and constant mistakes
• How to remember integrals logically (not by rote)
• How these functions appear in board exam questions
• How to write neat, step-wise solutions for full marks

This video acts as a **ready-made revision sheet explained in detail**.

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📚 *Chapter Details:*
Class: 12
Subject: Mathematics
Chapter: 7 – Integration
Topic: Integration of Important Functions
Board: CBSE | NCERT
Level: Board Exam Focused | High-Scoring

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🧩 *Coming Next:*
▶️ Mixed Integration Problems (Board Pattern)
▶️ Integration with Combined Methods
▶️ Full Chapter Revision Test

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💬 *Try This Question:*
Evaluate
\[
\int (3x^2 + \sin x + e^x)\, dx
\]
Comment your answer below 👇 — I’ll PIN the correct solution!

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