# A smart way to avoid a lot of Inverse hassle?

#### gerardhoyle

Hi, Calculus is about logic & it's great because
if you figure out the underlay of specific things
you can sidestep memorizing a heckload of
information.

To me the only hard thing is finding these tricks,
I'm specifically having a problem with integrating
inverse trigonometric functions.

For taking the derivative it's simple,

$$\displaystyle y = sin^{-1}(2x^2)$$

$$\displaystyle siny = 2x^2$$

$$\displaystyle cosy \cdot \frac{dy}{dx} = 4x$$

$$\displaystyle \frac{dy}{dx} = \frac{4x}{cosy}$$

$$\displaystyle \frac{dy}{dx} = \frac{4x}{\sqrt{1 - sin^2y} }$$

$$\displaystyle \frac{dy}{dx} = \frac{4x}{\sqrt{1 - 4x^4} }$$

and voila!

No memorizing whatever it is that litters up
the engineering book I foolishly bought.

However, for integrating these functions I don't see
the easy process.

Like, there are 6 functions all differing very slightly
and there's no way I'll be able to memorise them.
Every source I've checked tells me that because I know
the derivatives I can just reverse the process & copy
the form & write the integral. Yay!

Except, I'd have to go through up to a possible 6 side
calculations of derivatives to search out which
form my current integral is in so I can just magially
copy it.

Is there no better way than rote memorization?

Is there no simple logical model to follow that
generalizes to all 6 functions like taking derivatives
of them all has?

#### allsmiles

LoL, i found your comments very funny, but unless you buy a book, or look it up on the internet, i think the way you are doing it is the best way to do it, without messing up.

you could always look here Calculus Primer Calculus Tutorial

i looked at it and i thought it was so stupid, who knows, you may be a lucky person, unlike my. Lol #### gerardhoyle

LoL, i found your comments very funny, but unless you buy a book, or look it up on the internet, i think the way you are doing it is the best way to do it, without messing up.

you could always look here Calculus Primer Calculus Tutorial

i looked at it and i thought it was so stupid, who knows, you may be a lucky person, unlike my. Lol Lol thanks (Rofl)

That calculus primer tutorial looks more complicated than my lazy book! (Wondering)

If your having trouble with calc & have resorted to using that scary looking calculus primer site I found a huge list of links in some post on this site that you might like, I think they are great!

UCCS | Department of Mathematics (requires registration but is free)
http://www.sci.uidaho.edu/polya/math...=1&sec=1&sub=0