`int_(-pi/4)^(pi/4) (x^3 + x^4 tan(x)) dx` Evaluate the definite integral.

You may start by checking if the function `f(x) = x^3 + x^4*tan x` is an odd or even function, such that:

`f(-x) = (-x)^3 + (-x)^4*tan(-x) = -x^3 + x^4*(-tan x) = -x^3 - x^4*tan x = -(x^3 + x^4*tan x) = -f(x)`

Hence, the function `f(x) = x^3 + x^4*tan x` is an odd function and you may use the following property, such that:

`int_(-a)^a f(x) dx = 0` , if f(x) is odd

Hence, according to this property, `int_(-pi/4)^(pi/4) (x^3 + x^4*tan x)dx = 0.`