Improper Integrals / Antiderivatives.

[mortokr]

Homework Statement

Evaluate each improper integral whenever it is convergent.

1. S 1-infinity 4 / x

2. S 4 - infinity 2/x^3/2

Homework Equations

The Attempt at a Solution

I'm having trouble with antiderivatives. I understand how to do them when the problem is like x^4 + x^2 + 3 or something but anytime they're in like a fraction form I get lost and the first step in improper integrals is finding the antiderivative.

 

[rock.freak667]

well firstly do you know what is d/dx (lnx) gives?

Secondly 1/aⁿ = a^-n

 

[mortokr]

ln x = 1/x right?

So, 4/x would just be x2?

 

[rock.freak667]

d/dx(lnx) = 1/x right?

So, 4/x would just be x2?

No. If you differentiate lnx with respect to x to get 1/x, and integration is the reverse of differentiation, then the integral of 1/x with respect to x gives what?