Factorial Final Surge | JEE 2026 | JEE Mains 2026 + JEE ADV. 2026

Currently Playing: All Algebraic Integration Formats Covered | Indefinite Integration | JEE 2026

All Algebraic Integration Formats Covered | Indefinite Integration | JEE 2026 | Factorial Final Surge In this session of Factorial Final Surge, we complete the chapter Indefinite Integration by covering all important algebraic formats required for JEE Mains and JEE Advanced. This lecture focuses on pattern recognition, substitution techniques, algebraic manipulation, and partial fractions, which are extremely important for solving integration problems quickly in the exam. A variety of JEE-relevant problems are discussed so that students develop strong intuition for identifying the correct method in indefinite integration. If you master these formats, integration questions become much more predictable in JEE. Problems Discussed in the Video Rational Function (Partial Fractions) ∫ (x² + x + 1) / ((x − 1)(x − 2)(x − 3)) dx ∫ (2x² + 41x − 91) / ((x − 1)(x + 3)(x − 4)) dx Standard Algebraic Manipulation Formats ∫ dx / (x(x² + 1)) ∫ (x cosα + 1) / (x² + 2x cosα + 1)^(3/2) dx ∫ (ax² − b) / (x√(2c²x² − (ax² + b)²)) dx ∫ (x − 1) / (x²√(2x² − 2x + 1)) dx ∫ (x² − x⁻²) / √(x⁴ + x² + 1) dx Substitution Based Integrals ∫ x⁷ / (1 − x²)⁵ dx ∫ x / (1 − x⁴)^(3/2) dx Root and Linear Substitution Formats ∫ dx / ((2x + 1)√(4x + 3)) ∫ dx / ((x + 1)√(1 + x − x²)) ∫ dx / ((x² + 5x + 2)√(x − 2)) ∫ dx / ((x² + 4)√(4x² + 1)) Special Algebraic JEE Formats ∫ (x² + 1) / (x⁴ + kx² + 1) dx ∫ (x² − 1) / (x⁴ + kx² + 1) dx ∫ (x + 1)² / (x⁴ + x² + 1) dx ∫ dx / (x⁴ + a⁴) Substitution and Pattern Recognition ∫ (2x − 1) / √(4x² + 4x + 2) dx ∫ x / (x⁴ + x² + 1) dx ∫ (3eˣ + 5e⁻ˣ) / (4eˣ − 5e⁻ˣ) dx Rational Decomposition ∫ (2x² − 5) / (x⁴ − 5x² + 6) dx ∫ x³ / (x⁴ + 3x² + 2) dx ∫ (x³ + x − 1) / (x² + 2)² dx ∫ (x³ − 2x² + 4) / (x²(x − 2)²) dx ∫ x / ((x² + 2)(x² + 1)) dx This session completes the algebraic integration toolkit required for JEE Main and Advanced. Mastering these patterns will significantly improve speed, accuracy, and confidence in integration problems. Join the Factorial Academy Telegram community for discussions and updates https://t.me/academyfactorial #JEE2026 #JEEMains2026 #JEEAdvanced2026 #JEEMaths2026 #IndefiniteIntegration #Integration #JEEMaths #FactorialAcademy