Why Your U-Substitution Failed on This Integral скачать в хорошем качестве

Why Your U-Substitution Failed on This Integral

👇 FREE Study Guide 👇 Crush your next exam! Subscribe to my newsletter to get your free guide AND MORE: https://www.numberninjasmaths.com/#ne... 🎮 Master Math with my NEW Number Ninjas Math Game! 🎮 I created this fun, family-friendly math puzzle game (not calculus) to help you level up your math skills on iPhone / iPad! Check it out: https://tinyurl.com/NumberNinjasGame ⭐ Support the Ninjas! ⭐ Become a Member: Get MORE guides & goodies! https://tinyurl.com/JoinTheNinjaDojo Ninja Swag: Rock the look, grab a mug & more! https://tinyurl.com/NumberNinjaDaveStore 📚 Recommended Math Tools & Resources 📚 (Affiliate Links Below - As an Amazon Associate, I earn from qualifying purchases. Helps support the channel!) Conquer Exam Anxiety: Take care of YOU! https://amzn.to/3Y2LWKv Crush the AP Calculus Exam: Dominate the test! https://amzn.to/4ilFe9K Ultimate Calculus Calculator: This thing is a BEAST! https://amzn.to/4eBNeRS Precision Ruler: Super precise & handy! https://amzn.to/4doupRk 🛠 My YouTube Toolkit 🛠 I use VidIQ to make better videos for you! Check it out (I get a small commission): https://vidiq.com/numberninjadave Struggling with integrals that have e^x under a square root? You've come to the right place. In this video, we'll solve the integral of 1/sqrt(1+e^x), a problem that looks intimidating but is actually a perfect example of a clever u substitution. We'll walk through the exact substitution to use, how to handle the dx term, and how it simplifies into a partial fractions problem. This tutorial is great for any calculus student who wants to get better at spotting the right u-substitution and wants to build the confidence to solve more advanced integrals. 0:00 - The Problem & Why It's a Headache 0:28 - The Common Mistake (And Why It Fails) 0:42 - The Correct Approach: Isolate 'x' First 1:23 - Taking the Derivative to Find 'dx' 1:50 - Substituting and Simplifying the New Integral 2:18 - Setting Up the Partial Fraction Decomposition 2:48 - Solving for Constants A and B 3:27 - Rewriting and Integrating the Two Fractions 4:02 - Substituting 'u' Back In