Stuck on a step

  • Thread starter asdf1
  • Start date
  • #1
734
0

Main Question or Discussion Point

i'm trying to solve an equation, but i'm stuck on this step:
(integral sign) e^2x*e^x(3sin2x+2cos2x)dx =?
 

Answers and Replies

  • #2
574
0
use the exponential form for the trig functions and multiply through. you'll get a few easy integrals of the form
[tex]\int e^{(a+ib)x}dx[/tex]
 
  • #3
arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,970
132
If you don't know about the complex exponential, here's a technique using integration by parts (I'll let you tailor it to your specific example):
Suppose you are to find an anti-derivative (i.e, indefinite integral) of the function [tex]f(x)=e^{x}\sin(x)[/tex], that is, you are to find J, where J is given as:
[tex]J=\int{e}^{x}\sin(x)dx(1)[/tex]
The right-hand side can now be rewritten as:
[tex]\int{e}^{x}\sin(x)dx=e^{x}\sin(x)-\int{e}^{x}\cos(x)dx=e^{x}\sin(x)-e^{x}\cos(x)-\int{e}^{x}\sin(x)dx=e^{x}\sin(x)-e^{x}\cos(x)-J(2)[/tex]
where I have used integration by parts twice, along with (1).
Thus, we have:
[tex]J=e^{x}\sin(x)-e^{x}\cos(x)-J\to{J}=\frac{e^{x}\sin(x)-e^{x}\cos(x)}{2}[/tex]
(I've not bothered with the constant of integration; this should also be included in the final expression).
 
  • #4
734
0
ok, thanks! i'll try that~
 
  • #5
734
0
come to think of it... is there a quicker way?
 
  • #6
arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,970
132
Sure; we've got the "abra-kadabra" formula, but it is only taught to 50 year old professor with proven gentle disposition because of the formula's potential for abuse.
 
  • #7
734
0
haha... thanks! :)
 

Related Threads on Stuck on a step

  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
13
Views
2K
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
1K
Replies
7
Views
4K
  • Last Post
Replies
6
Views
2K
Replies
2
Views
7K
  • Last Post
Replies
1
Views
4K
Replies
3
Views
3K
Top