1.1 | Differential Equations | Integration By Substitution Methods

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1.1 | Differential Equations | Integration By Substitution Methods

#differentialequations #calculus #appliedmathematics #engineeringmathematics

In this video, we'll go through three numerical based on integration by substitution methods.

By the end of this video, you'll have a reasonable idea of solving integration by the method of substitution.

So, let us investigate this fascinating topic and broaden our knowledge.

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Formula Sheet

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Time Stamp:

00:05 Three Problems
00:13 Methods of Integration - Integration by Substitution (Problem 1)
01:23 Methods of Integration - Integration by Substitution (Problem 2)
02:24 Methods of Integration - Integration by Substitution (Problem 3)

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... Good day to you, The 3rd integral can also be solved as follows ... INT[1/(e^X + 1)]dX .... rewrite the numerator as follows ... 1 = e^X + 1 - e^X ... INT[ (e^X + 1)/(e^X + 1) - e^X/(e^X + 1) ]dX .... INT[ 1 ]dX - INT[ e^X/(e^X + 1) ]dX ... applying INT[ F'(X)/F(X) ]dX = LN I F(X) I + C on the 2nd integral ... X - LN I e^X + 1 I + C ... fascinating to see more strategies to solve the same problem ... thanking you sir for showing me a new solution path for this integral ... Best regards, Jan-W

jan-willemreens

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