Question

What is `int_(0)^(oo) 6/x^4 - 2/x^3 dx`?

Answer 1

The integral does not converge. (It diverges).

Explanation:

`int(6/x^4-2/x^3) dx = -2/x^3+2/x^2 = (2(x-1))/x^3`

So

`lim_(ararr0^+) int_a^1(6/x^4-2/x^3) dx = lim_(ararr0^+)(2a-2)/a^3=oo`
.