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

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    Integral
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Discussion Overview

The discussion revolves around the calculation of the integral of sin(ln x), focusing on the methods and techniques involved in solving this integral, including substitution and integration by parts. The context includes homework-related inquiries and procedural clarifications.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant seeks help with the procedure to calculate the integral of sin(ln x) and expresses difficulty in reaching the provided result.
  • Another participant suggests using the substitution x = e^z to transform the integral.
  • A request for detailed procedural steps is made, indicating that the teacher mentioned the use of integration by parts.
  • A participant explains that the substitution leads to the integral ∫ e^z sin(z) dz and mentions that integration by parts is the method to solve it.
  • One participant suggests that two applications of integration by parts would be necessary for the transformed integral.
  • A participant corrects the notation from "In" to "ln," expressing frustration over the common misuse of the terms.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and approaches to the problem, with no consensus on the best method or clarity on the steps involved in the integration process.

Contextual Notes

There is an indication that the discussion may involve missing assumptions or steps in the integration process, particularly regarding the application of integration by parts and the transformation of the integral.

kennis2
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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,
 
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Use the substitution x = e^z.
 
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?
 
Last edited:
Well making the substitution x = e^z changes the integral to the following:

[tex]\Int e^z Sin(z) dz[/tex]

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

[tex]\int \ln\sin x \ dx[/tex]

Daniel.
 
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!)
 

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