Wednesday, December 3, 2014

Advanced Math Solutions – Integral Calculator, inverse & hyperbolic trig functions

In the previous post we covered common integrals (click here).  There are a few more integrals worth mentioning before we continue with integration by parts; integrals involving inverse & hyperbolic trig functions. We kept these for later, as they are usually used with substitution.

  • \int \frac{1}{x^2+1}dx=\arctan \left(x\right)+C
  • \int \frac{1}{\sqrt{1-x^2}}dx=\arcsin \left(x\right)+C
  • \int \frac{1}{1-x^2}dx=\arctanh \left(x\right)+C
  • \int \frac{1}{\sqrt{1+x^2}}dx=\arcsinh \left(x\right)+C


Let’s take a look at a few examples, notice that we are trying to manipulate the functions to a known form (can be tricky)


Here’s an example using algebraic manipulation and substitution (click here):



Here’s another example using substitution to get to the common form (click here):



Here’s another example using substitution to get to the common form (click here):



Ready for integration by parts!


Cheers,
Michal

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