Integrals of the form 1/(a2+x2) and 1/√(a2-x2)

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Lesson:

You should be familiar with the standard integrals

$\displaystyle\int \dfrac{1}{a^2 + x^2} \dx = \dfrac{1}{a} \tan^{-1} \left( \dfrac{x}{a} \right) + c$
$\displaystyle\int \dfrac{1}{\sqrt{a^2 - x^2}} \dx = \sin^{-1} \left( \dfrac{x}{a} \right) + c$

In these videos I show you how we can reduce integrals to this form.

Completing the square and substitution types

I now show you how we can complete the square and use substitution to convert some integrals in to the above forms

Care must be taken when it comes to working with limits when using these integrals