# Homework Help: Evaluate using any method: Essentials Of Calculus

1. Aug 2, 2010

### Nawz

1. The problem statement, all variables and given/known data

$$\int\frac{ [(lnx)^3 - 4(lnx)^2 + 5]}{x}$$dx

2. Relevant equations

3. The attempt at a solution

xlnx^4 - (4/3x)lnx^3 +5x^2

my attempt at a soultion was all wrong. The divided by x is confusing me on this one.

The right answer is: ((lnx)^4/4) -(4/3)(lnx)^3+5lnx+C

Last edited: Aug 2, 2010
2. Aug 2, 2010

### rock.freak667

(You forgot the 'dx' in your integral)

but if you let u=lnx, what is du =?

3. Aug 2, 2010

### Nawz

It would be 1/x

What is the point of the dx after it too: is it just there for the added C?

I got this right now and it is close:

$$\int\frac{(u)^3-4(u)^2+5}{x}$$dx

$$\frac{(u)^4/4-(4/3)u^3+5x}{x}$$ + C

I guess that 5x is suppose to be a U but I don't know why. I still have it divided by x too?

4. Aug 2, 2010

### rock.freak667

In your integral, it means what you are integrating with respect to.

so if du/dx = 1/x, then that means that du = (1/x)dx.

Do you see where you will have '(1/x)dx' to replace with 'du'?