In this video I go over a useful trig identity which is basically that the integral of 1/(x^2+a^2) = 1/a*arctan(x/a). This identity is derived from the derivative of arctan(x) or inverse tan(x) which I covered in my earlier video and you can see that proof in the video link below. This identity is used a lot when finding the integrals of rational functions that require using partial fraction decomposition to simplify the integral.
Download the notes in my video: http://1drv.ms/1Jjvn1o
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/trigonometric-identity-integral-of-1-x-2-a-2
Related Videos:
Derivative Rules: Proof of Chain Rule:
Derivative of arctan(x) or Inverse tan(x):
Integration by Partial Fractions: Example 5: .
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I don't always prove trigonometric integral identities but when I do I usually use the derivative of a similar function in proving it ;)
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/trigonometric-identity-integral-of-1-x-2-a-2