I need help finding this integral. I think my algebra may be wrong which is why it isn't coming out right. Could you please help and correct me?

Question

Find the integral. Use C for the constant of integration.

∫ 1/√1-(2z)² dz

I thought that I could take the root of each of the parts in the denominator and I got 1/1-(2z)  and then I got z/z-z² but that was marked wrong. Could you please help me figure this one out please?

Answer 1

Indeed you made an error when attempting to take square root of a difference by square rooting each term!

No can do.

 

As for the antidifferentiation: Look for a pattern in relation to arcsin...

In my Calculus book, this integral is given in the Table of Integration, in the part called Forms involving sqrt (a² - u²).

You will have to take into account the factor 4...