Let U = tan⁻¹x.

Use Integration by Parts;
If f(x) = x and dg = cosx dx,
then df = ___ and g(x) = ____.

Evaluate and solve.

$=f(x)g(x)\Big|_0^\pi-\int_{0}^{\pi }g(x)df$

Write this integral as the sum of two improper integrals.

$\lim_{a\rightarrow 2^{-}}\int_{0}^{a}\frac{dx}{(x-2)^{\frac{2}{3}}}+\lim_{a\rightarrow 2^{+}}\int_{a}^{4}\frac{dx}{(x-2)^{\frac{2}{3}}}$