# Agglomeration Of Tricks

Calculus Level 5

$\large \dfrac14 \int_0^1 \dfrac{t (1-t)}{1+t^2(1-t)^2} \, dt = \Re(-z \tan^{-1} z )$

If the equation above holds true, where $$z$$ is a zero of a polynomial with integer coefficients, find $$|z|^{-4}$$. 

Clarification: $$\Re(x)$$ denotes the real part of the complex number $$x$$. For example, $$\Re(3+4i) = 3$$.

×