Integration by Partial Fractions | Irreducible Quadratic Factor | Step-by-Step Tutorial
n this video, we explore Integration by Partial Fractions when the denominator contains an irreducible quadratic factor — a type of term that cannot be factored into real linear expressions, like ( 𝑥 2 + 4 ) (x 2 +4), ( 𝑥 2 + 𝑥 + 1 ) (x 2 +x+1), etc. This is a step-by-step calculus tutorial designed to help students understand how to break down rational functions and integrate them easily using partial fractions. Irreducible quadratics require a different approach than linear or repeated factors, and we’ll show you exactly how to handle them. 📚 In this lesson, you’ll learn: ✔️ What an irreducible quadratic factor is ✔️ How to set up the correct partial fraction form using Ax + B in the numerator ✔️ Solving for constants using substitution or equating coefficients ✔️ How to integrate rational expressions that result from the decomposition ✔️ Tips for completing the square if needed 🧠 Perfect For: • Class 11–12 (FSc, A Levels, AKUEB, CBSE) • University Calculus Students • Anyone reviewing rational function integration • Students preparing for competitive exams (SAT, ACT, ECAT) 📘 Example Covered: We solve an integral like: ∫ 3 𝑥 + 2 𝑥 2 + 4 𝑑 𝑥 ∫ x 2 +4 3x+2 dx and show how to rewrite and integrate it properly. ⏱️ Timestamps: 0:00 – Introduction 0:40 – What is an irreducible quadratic? 1:30 – Setting up the partial fraction form 3:00 – Solving for unknowns 5:00 – Integration process explained 7:00 – Final answer with explanation 🔔 Like, share, and subscribe for more math tutorials, especially if you're preparing for board exams or university entrance tests! WATCH NEXT: Entery test prepartion videos series for Engineering • Set and Venn diagram MCQS video 1 Mathemat... class 9th mathematics video series • identify the sets denoted by N, Z, W, O, P... class 10th mathematics video series • Frequency distribution table class 11th mathematics video series • introduction to graph of trigonometry func... class 12th mathematics video series • Video class 9th AKUEB mathematics past paper video series • CLASS 9TH AKUEB PAST PAPER 2011 class 10th AKUEB mathematics past paper video series • CLASS 10th AKUEB past paper 2011 video 1 class 11th AKUEB mathematics past paper video series • class 11 AKUEB past paper MCQs 2012 video 1 class 12th AKUEB mathematics past paper video series • PAST PAPER 2011 AKUEB CLASS 12 Class 9th akueb topical past paper • "AKUEB Class 9 | Topical Past Paper Soluti... Class 10th akueb topical past paper • "AKUEB Class 10 | Topical Past Paper Solut... Cambridge AS Level Pure Mathematics 1 Playlist • Cambridge AS Level Pure Mathematics 1 Play... IGCSE Mathematics (0580) & O Level Mathematics (4024) video learning series • O Level Mathematics (4024) learning series FACE BOOK PAGE / mathsekhta.hai YOUTUBE CHANNEL / @mathsbydoing Whatapk channal https://whatsapp.com/channel/0029Vb5y... If you like this video subscribe my channel . Keep supporting me so I can continue to provide you with free content. Thanks FOR CONTACT ME [email protected] What apk number +923133097014
