Integration & Natural Log Functions Examples | Calculus - JK Math

Example Problems For How to Integrate Rational Functions Using the Natural Log Rule (Calculus) ➡️ Download My Free Calculus 1 Worksheets: https://www.jkmathematics.com/calculus1-worksheet-set 🖥️ Join My Membership Site: https://www.jkmathematics.com/plus In this video we look at practice problems of integrating various rational functions using the Log Rule of Integration. Previously we discussed how the power rule of integration did not apply to functions likes x^-1, also written as 1/x. We can now integrate theses functions using the log rule of integration, which comes from reversing the derivative of the natural log function, ln(x). This includes an example of a rational function that requires using long division. Additionally, we look at examples of using the new integration rules for individual trigonometric functions we did not previously know how to integrate that stem from the log rule for integration. We look at various examples and practice integrating using these new rules. This course is designed to help students understand the concepts of calculus at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with each lesson under 20 minutes! Calculus requires a solid understanding of precalculus and algebra concepts and techniques including factoring, equation manipulation, trigonometric equations, logarithms, finding slope, graphing, and many more. If you are not familiar with these prerequisite topics, be sure to learn them first! Video Chapters: 0:00 Example 1 - 8/x 1:57 Example 2 - 3/(3x+2) 4:19 Example 3 - x^2/(x^3+1) from 0 to 2 8:30 Example 4 - (x^2-2x-8)/(x+1) 13:57 Example 5 - 1/(x*ln(x^4)) 16:26 Example 6 - csc(theta/pi)/pi 📝 Lesson Video For These Examples: https://youtu.be/JLFGQ9npPAU ⏩ Next Lesson: https://youtu.be/QoA2VUTSIss 📺 Course Playlist: https://youtube.com/playlist?list=PLHdRLeAbIZE6krGDQthaQRpLZFLD4ob54 🌐 Visit My Website: https://www.jkmathematics.com ⚡️Math Products I Recommend⚡️ Graphing Calculator: https://amzn.to/3XuUcB9 Non-Graphing Calculator: https://amzn.to/46hHJ7E Financial Calculator: https://amzn.to/3CRe9s4 Graphing Paper: https://amzn.to/46mAfAr College Rule Paper: https://amzn.to/3NOJaTN My Favorite Pencil: https://amzn.to/3NOFMIB My Favorite Erasers: https://amzn.to/3PumUQB Calculus Workbook: https://amzn.to/3r8SnNP ⚡️Textbooks I Use⚡️ Calculus 1 & 2: https://amzn.to/3PzfI5F Calculus 3: https://amzn.to/46rSy76 Financial Mathematics: https://amzn.to/3ppIVW0 ⚡️My Recording Equipment⚡️ iPad Air: https://amzn.to/3phEug1 Apple Pencil (Gen 2): https://amzn.to/3Nl45MM Tablet Desk Stand: https://amzn.to/4420rPh External Hardrive: https://amzn.to/44pkEyh (Commissions earned on qualifying purchases) Find me on social media: Facebook: https://www.facebook.com/jkmathematics Twitter: https://twitter.com/jk_mathematics Instagram: @jk_mathematics Found this video to be helpful? Consider giving this video a like and subscribing to the channel! Thanks for watching! Any questions? Feedback? Leave a comment! -Josh from JK Math #calculus Disclaimer: Please note that some of the links associated with the videos on my channel may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.