Having troubles integrating e^(2x)sin(x)

  • #1
Hi, I have to integrate this:

[tex]
\int e^{2x}sinx
[/tex]

I've tried by parts, but [tex]e^{2x}[/tex] never goes away and [tex]sinx[/tex] just keeps going back and forth to [tex]cosx[/tex]. Is there some kind of substitution I should use? The original question was the differential:

[tex](-e^xsinx+y)dx+dy = 0[/tex]

and I'm trying to find the integration factor to solve for [tex]y[/tex], but I can't seem to figure out how to integrate it. Thanks!
 

Answers and Replies

  • #2
644
1
for your first question,
proceed with the integration by parts ....
label the original integral as I and continue
at some stage, u will have,
I = e^x something + something - I (or something like that)
rearrange to find I.

-- AI
 
  • #3
102
0
To clarify, keep integrating by parts untill you get your original integral. then move that integral to the other side of the equation and solve :D
 
  • #4
1,789
4
Hi

Use the ILATE rule which tells you which function to take as the first one. ILATE = Inverse Circular Function, Logarithmic Function, Algebraic Function, Trigonometric Function, Exponential Function (this is the order...the function appearing higher in the list should be taken as the first function).

Cheers
Vivek
 

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