Help with calculus problem?

Question

Evaluate the integral: Where as the limits of integration are from 0 to 1.

1 4x^3 (1 + x^(4(2006)))
∫ __________________ dx
0 (1 + x^4)^2008

Answer 1

Let u = 1+x^4 --> du= 4x^3dx
So intergral becomes
1 u^2006
∫ ________ du =
0 (u)^2008
1
∫ u^-2 du =- u^-1 = -1/u = -1/(1+x^4)=
0
-1/(1+1^4) - (-1/1) = 1/2