I dont know why but I am blanking on how to do this one
$\displaystyle \int\frac{x^{\frac{1}{4}}}{1+\sqrt{x}}dx$
I know its sad...it will be something obvious...I tam thinking trig sub?
Let me see if I can tell what you are thinking
$\displaystyle \frac {4u^4}{1 + u^2} = \frac {4u^4 - 4 + 4}{1 + u^2} = \frac {4u^4 - 4}{1 + u^2} + \frac {4}{1 + u^2} =$ $\displaystyle \frac {4(u^2 + 1)(u^2 - 1)}{1 + u^2} + \frac 4{1 + u^2} = 4u^2 - 4 + \frac 4{1 + u^2}$
That wasn't so bad ...it was even easier knowing the EmptySet's final form to work towards...