00:01
We know that the 1 over square root of the 1 minus x square can be written down as 1 plus minus x square power of a half minus a half and here we can apply the binomial theorem and then we should get equal to summation of and goes from zero to infinity and now inside we have this only be the value a so we be minus one half and then choose n and then we will have the minus x square power n and it will equal to the summation and and actually infinity and we have here will be minus one half choose n, minus 1 power n, x power n.
01:02
So it means that we can rewrite everything by this equal to summation of n goes from zero to infinity and minus one half choose n and minus one power n x power n and now if we do the integrate on both sides, integral on both sides, dx, integral of both sides and the x here.
01:31
On the left hand side here we got the side inverse of the x plus content c equal to, here we got the summation and goes from 0 to infinity, minus 1 half, choose n, and minus 1 power n, integration of the x and dx, so equal to the summation end goes from 0, 0 ,000, and 0 ,000, which infinity, minus one half, choose n, minus 1 power n, and then we will have the x power m plus 1 devalued n plus 1.
02:10
And for the c, we can send the x equal to 0, so side inverse of the 0 plus c will equal to everything here will equal to 0, if x equal to 0.
02:25
So if x equal to 0, 0 will be 1, it will be 0 as well...