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Discovery Project: Patterns in Integrals: Question 4: x^n * e^6

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First published at 20:12 UTC on August 2nd, 2019.

Math Easy Solutions

MES

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In this video I go over another Question in the Patterns in Integrals Discovery Project and this time go over the family of integrals with integrand x^n * e^x where n is a positive integer. Like in the other questions, I use a Computer Algebra System (CAS) to solve multiple integrals with that form and based on the pattern of the answers guess a formula for the general form of the integral. I also use a CAS to calculate the general form but that answer involves the Gamma function, Γ(x) = (x-1)!, but that topic is beyond what I have covered thus far so it is shown as reference only in the video. I also prove the guess made from the pattern of integral answers using the Principle of Mathematical Induction. This is an important video to understand the power of computers in determining integral formulas for entire families of integrals as well as understanding mathematical induction so make sure to watch the video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIheRJ_xGwQn2_V5zjqA

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/discovery-project-patterns-in-integrals-question-4-x-n-e-6

Related Videos:

Discovery Project: Patterns in Integrals: Question 3: x^n * ln(x): http://youtu.be/PA9-Me1ko10
Discovery Project: Patterns in Integrals: Question 2: sin(ax)cos(bx): http://youtu.be/O0p1DGMOcfM
Discovery Project: Patterns in Integrals: Question 1: http://youtu.be/uQUu0XFMw8I
Integration using Tables of Integrals: Example 1: http://youtu.be/AOToFP-4Mfg
Can We Integrate All Continuous Functions?: http://youtu.be/OFEDLJYqYps
Factorials - i.e. 4! = 4*3*2*1 = 24: http://youtu.be/SWnrhDOLQgA
Problems Plus Example 4 - Mathematical Induction: http://youtu.be/WdIr_onvUtE .

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