Calculus - Using i to evaluate an integral

In this video we use i to help break up our function so we can do a partial fraction decomposition. This allows all of our factors to be nice linear terms. Note that this is not contour integration, rather just factoring and using i as a constant to make anti-derivatives nice and simple.
▬▬ Chapters ▬▬▬▬▬▬▬▬▬▬▬
0:00 Start
0:32 Example
0:44 Partial fraction decomposition
1:40 Determine the unknown coefficients
4:53 Solving a system of linear equations
6:39 Taking the anti-derivative
7:33 Simplify the expression
9:22 Evaluate the expression at the bounds
10:48 Writing the final answer
11:18 Wrap up information and ending
▬▬ Related Videos ▬▬▬▬▬▬▬▬▬▬▬
This video is related to many other topics. Check them out:
The basics of indefinite integrals: • Calculus - The basics ...
Partial fraction decomposition: • Pre-Calculus - Partial...
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[@AvoidsPikes-]

I've never liked doing any math, ANY math with the imaginary number i. I liken that number to driving in heavy traffic on a street during rush hour in a rainstorm while that street is being repaired by repairmen. Thanks MySecretMathTutor for another great video. I also forgot that the antiderivative of 1/x is ln(x), so I just got a bit of a refresher.

[@MySecretMathTutor]

Great to hear. Guess I should do a few more with the imaginary number so those streets can feel more well traveled. :^D

[@alchemysticwitch]

hi

[@seenurao5295]

Instead of that why don’t we substitute x=tan

[@MySecretMathTutor]

You could for this one, but I wanted to specifically wanted to show how you might use the number i, without going down the road of contour integrals. :^D