|| Indefinite Integration || JEE Mains || Video - 2 || Method of Substitution || скачать в хорошем качестве

|| Indefinite Integration || JEE Mains || Video - 2 || Method of Substitution ||

Welcome back to FactorXMaths! This is the second video in our Indefinite Integration for JEE Main 2026 playlist. I’m Akshat Agarwal from IIT Kharagpur, and in this session we dive into one of the most important JEE techniques: integration by substitution, which is basically the reverse of the chain rule from differentiation. 🔹 What’s inside this video? Idea of substitution (reverse chain rule): We first understand when an integral has the hidden form ∫f(g(x)) g′(x)dx and how setting t=g(x) can turn a scary-looking function into a simple standard form. You’ll see why “change of variable” is the heart of this method and how it connects back to the formulas from Video 1. Direct substitution patterns: Classic JEE forms like ∫f′(x)/f(x)dx, ∫f′(x)/ f(x) dx, and integrals of the type ∫f(ax+b)dx, where a simple linear or functional substitution directly reduces the integral to a known standard type. We’ll solve multiple examples so you can recognize these patterns instantly in the exam. Standard special substitutions: Important “ready-made” substitutions used repeatedly in JEE How to decide the right substitution: A clear checklist-style thought process: look for inner function + its derivative, complicated roots, quadratics in denominator, or composite trig expressions, then test 1–2 natural substitutions instead of randomly guessing. JEE-style examples and pitfalls: We solve a variety of exam-level indefinite integrals by substitution, discussing common mistakes like forgetting to change limits (for definite integrals later), missing the derivative factor, or not converting everything to the new variable. This makes the method feel like a predictable toolkit, not trial-and-error. By the end of this video, integration by substitution will feel like a systematic pattern-recognition game rather than guesswork, and it will set you up perfectly for the next video on integration by parts. 📌 Don’t forget to: 👍 Like the video if substitution feels more natural now 🔔 Subscribe and turn on notifications for the next video on Integration by Parts 📂 Share this with friends who keep getting stuck deciding “which substitution to use” in integrals