How Do You Integrate sin(2x) e^(sin x)?

  • Context: Graduate 
  • Thread starter Thread starter biogoal123
  • Start date Start date
  • Tags Tags
    Integrating
Click For Summary

Discussion Overview

The discussion revolves around the integration of the function sin(2x) e^(sin x). Participants explore different methods for solving the integral, including integration by parts and trigonometric identities.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty with the integration problem and questions their approach after attempting integration by parts.
  • Another participant suggests using the double angle formula to expand sin(2x) as a potential strategy.
  • A later reply indicates that the participant realized a mistake in their choice of terms for integration by parts, leading to a successful integration after correcting their approach.
  • Another suggestion is made to use the substitution u = sin x as an alternative method for solving the integral.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a single method for solving the integral, as multiple approaches are discussed without resolution on which is preferable.

Contextual Notes

Some participants' approaches depend on specific choices of terms for integration by parts, which may not be universally applicable. The discussion does not resolve the overall effectiveness of the suggested methods.

biogoal123
Messages
4
Reaction score
0
hey guys I am absolutely stumped on this one integration problem:

it asks us to integrate sin (2x) e ^ (sin x)

i integrated by parts once and was left with an even larger term to integrate, which leads me to believe that i might be doing it wrong

any help is appreciated, thanks
 
Physics news on Phys.org
Try expanding sin(2x) using a double angle formula.
 
wow ok i feel like an idiot. when i split it into double angles i had (2 sin cos e^sin) and i kept having my two terms for integration by parts being (cos sin) and (e ^ sin) instead of the VERY OBVIOUS one which i kept missing which was (sin) and (cos e ^sin) which gave a very nice and smooth integration

thanks again
 
You could also have done a substitution u = sin x.
 

Similar threads

High School Straightforward integration…
  • · Replies 27 ·
Replies
27
Views
3K
Undergrad Why is the integral of ##\arcsin(\sin(x))## so divisive?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Did Math DF's integral calculator make a glaring mistake?
  • · Replies 8 ·
Replies
8
Views
4K
Undergrad Integration of ##e^{-x^2}## with respect to ##x##
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Integrating a product of exponential and trigonometric functions
  • · Replies 21 ·
Replies
21
Views
4K
High School How Do You Derive the Formula for sin(x-y)?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Different Substitution for Solving an Integral
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Ambiguity of the term "indefinite integral"
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Gaussian integral by differentiating under the integral sign
  • · Replies 19 ·
Replies
19
Views
5K
Undergrad Integrating sqrt(x) cos(sqrt(x)) dx
  • · Replies 8 ·
Replies
8
Views
5K