# How to integrate int sin(ln(x)) ?

1. Jun 15, 2009

### Shaybay92

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

I am having trouble solving the following:

$$\int$$sin(lnx) dx

3. The attempt at a solution

I let u = ln x but this makes xdu = dx so I am left with

$$\int$$x sinu du

2. Jun 15, 2009

### Cyosis

Re: Integration

That's the substitution you want to use,but you can't leave the x in there. If u=lnx, then x is?

3. Jun 15, 2009

### Shaybay92

Re: Integration

Would x = u2?

$$\int$$ue sin u du

Then do you do it by parts or something?

4. Jun 15, 2009

### Cyosis

Re: Integration

How on earth did you get that? Can you solve $u=\ln x$ for x?

5. Jun 15, 2009

### Shaybay92

Re: Integration

Oops I meant e^u, is that right?

6. Jun 15, 2009

### Cyosis

Re: Integration

Yes that's correct. You can now use integration by parts, twice.

7. Jun 15, 2009

### Shaybay92

Re: Integration

does e(lnx) cancel to 1?

8. Jun 15, 2009

### Cyosis

Re: Integration

No and you should really know that at this stage! If a function has an inverse, $f^{-1}(x)$, then $f^{-1}(f(x))=f(f^{-1}(x))=x$. So what is $e^{\ln x}$ and $\ln e^x$?