# Integral of sin(Inx)? help pls!

1. Apr 19, 2005

### kennis2

Hi I hope you can help me because I got test in this Thursday :(

What´s the procedure to calculate Integral of sin(Inx)?

The result is: (x/2){[cos (ln x)] - [sin (ln x)]} + C

But I never get there…

Thanks,

2. Apr 19, 2005

### Crosson

Use the substitution x = e^z.

3. Apr 19, 2005

### kennis2

can you so kind to do some procedures? cuz i dont get it :(
the teacher says this should be by parts..do u know how?

Last edited: Apr 19, 2005
4. Apr 19, 2005

### Crosson

Well making the substitution x = e^z changes the integral to the following:

$$\Int e^z Sin(z) dz$$

The way to solve this integral is by working backwards from the product rule, which is called integration by parts. I'm sure that your calculus book has an example, here is an abstract overview of the technique:

http://mathworld.wolfram.com/IntegrationbyParts.html

5. Apr 19, 2005

### dextercioby

Two times part integration will do the transformed integral.It would have been much nicer

$$\int \ln\sin x \ dx$$

Daniel.

6. Apr 20, 2005

### HallsofIvy

By the way, it is ln x NOT In x.

Am I the only person who gets really teed off by that?

(Sorry, but I have been seeing students writing "In" for "ln" for more years than I want to remember!)