TITLE: Taking an integral of an integrand consisting of different power radical functions
QUESTION [11 upvotes]: So I have this integral, $$\int_0^1 (1-x^7)^{1/3}-(1-x^3)^{1/7} dx$$ 
and  I don't know where to start with this. I tried  doing some Algebra, but I'm not recognizing any patterns. (Maybe it is my tired brain, but I'm completely lost.)
If any of you can point me in the right direction, give me some useful hints, or explain how to solve it, I would be forever grateful. 
Thank you!

REPLY [6 votes]: HINT:
If $(1-x^7)^{1/3}=y,y^3+x^7=1$ and if $x=1,y=0;$ if $x=1,y=0$
and if $(1-x^3)^{1/7}=y,y^7+x^3=1$ and if $x=1,y=0;$ if $x=1,y=0$
So, both represent the same area of the curve between $[0,1]$