# Integrals and such

1. Jun 18, 2005

### rachmaninoff

What methods or tricks are there to approach antiderivatives, beyond what's learned in Calculus II? I'm just talking about ordinary, analytic stuff like $$\int \sqrt{ \tan x } dx$$ not requiring 'special' functions. I mean, the integral tables were around for a while, right, so how did they solve all those things?

edit: by 'beyond Calc. II' I mean other than things like
-clever substitutions
-method of partial fractions
-integration by parts
-series expansions
etc.

2. Jun 18, 2005

### dextercioby

Yes to all of them.You'll have to "feel" it.For example,your integral won't definitely lead anywhere by parts,because the second integral will be uglier,as it will have an "x" and trigonometrical functions.So the way to do it is to use a sub which will throw away the sqrt.

$$\tan x=y^{2}$$

Daniel.