Integration & Natural Log Functions | Calculus Lesson 44 – JK Math

How to Integrate Rational Functions Into Natural Log Functions (Calculus Lesson 44)

➡️ Download My Free Calculus 1 Worksheets: https://www.jkmathematics.com/calculus1-worksheet-set

🖥️ Join My Membership Site: https://www.jkmathematics.com/plus

In this lesson we learn how to integrate 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). Additionally, we see how this rule leads us to new integration rules for individual trigonometric functions we did not previously know how to integrate like tan(x), sec(x), and more! We look at various examples and practice integrating using these new rules, including a function that requires using long division to get in a form that we can integrate using the log rule.

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 Integral of 1/x?
1:43 Log Rule For Integration
2:19 Example 1 – Integral of 3/x
3:45 Example 2 – Integral of 1/(2x+1)
6:15 Example 3 – Integral of x/(x^2+7)
9:08 Example 4 Part 1 – Integral of (x^2+x-6)/x-2
10:52 Example 4 Part 2 – Long Division!
15:45 Example 5 – Integral of tan(x)
18:23 New Trig Integration Rules

📝 Examples Video: https://youtu.be/ZLx7EXReuKg

⏩ 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.