How to Calculate the Integral of sin(ln x)?

[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,

 

[Crosson]

Use the substitution x = e^z.

 

[kennis2]

can you so kind to do some procedures? because i don't get it :(
the teacher says this should be by parts..do u know how?

 

[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

 

[dextercioby]

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

\int \ln\sin x \ dx

Daniel.

 

[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!)