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