Question

\[\int \frac{1}{(1-u^{4})^{\frac{1}{4}}} du \]

Answer 1

This can't be calculated as an elementary function, but is something rather complicated.

Answer 2

http://www.wolframalpha.com/input/?i=integral+1%2F%281-u^4%29^%281%2F4%29+du

Answer 3

Can you tell me the integration of
\[\int \sqrt{tan(x)} dx\] ??

Answer 4

Let u = sqrt(tan x) and then create a rational function. You then need to use partial fractions and grind away at it a bit.

Answer 5

then what do??
\[\int \frac{2u^{2}}{1+u^{4}}\]

Answer 6

and how to solve first one

Answer 7

With respect to the integral you've just written down in u, you now need to be rather inventive with the denominator of 1 + u^4 and write it as
\[(u^2 + 1)^2 - (\sqrt{2}x)^2\]
Now apply difference of squares and a partial fraction decomposition.

With respect to the first integral, I don't have anything concrete for you other than the Wolfram solution. Even differentiating that answer to confirm it is the integral would be gruesome.

Answer 8

correction: all in u obviously
\[(u^2 + 1)^2 - (\sqrt{2}u)^2\]