Do you mean ?
hello, if possible hep with the following:
Q: By expanding (1-4x)^1/2 and integrating term by term, or otherwise, find the series expansion for arcsin(2x), when |x|<1/2, as far as the term in x^7.
A: I have done it by consequatively differentiating until the seventh order and then evaluating at x = 0 to produce the desired series.
However I am at a loss as to how to do it by "expanding (1-4x)^1/2 and integrating term by term"..
...I know its basic stuff but I would much appreciate any help!
Maybe you were asked to expand instead? Because in this case, it is quite obvious how the integral of this term is related to .