# Hard integral to me but you?

1. Apr 22, 2005

### kennis2

(edited need help) hard integral to me but you?

I tried much but i couldn't resolve.. :grumpy:
Integral of (1+ln(x))/xln(x) dx
thanks =)

Last edited: Apr 22, 2005
2. Apr 22, 2005

### arildno

Hint:
What is
$$\frac{d}{dx}(xlnx)=?$$

3. Apr 22, 2005

### kennis2

its 1/x right?

Last edited: Apr 22, 2005
4. Apr 22, 2005

### arildno

No, you must use the product rule:
$$\frac{d}{dx}(xln(x))=1*ln(x)+x*\frac{1}{x}=ln(x)+1$$
What does that tell you?

5. Apr 22, 2005

### kennis2

oh you are right!
I know the answer then, BUT
I WROTE MY EXERCISE BAD SORRY HERE GO AGAIN
integral of (sqrt(1+ln(x)))/xln(x) dx

Last edited: Apr 22, 2005
6. Apr 22, 2005

### GCT

Does this pertain to finding the arc length of a function? Also, try writing it out in latex, you'll probably get more responses.

7. Apr 22, 2005

### stunner5000pt

is this the question??

$$\frac{\sqrt{1+\ln x}}{x \ln x} dx$$?

in which case substitute ln x = u and solve away!