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

1. Aug 1, 2004

### haXadecimal

Hi, I have to integrate this:

$$\int e^{2x}sinx$$

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

$$(-e^xsinx+y)dx+dy = 0$$

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

2. Aug 1, 2004

### TenaliRaman

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. Aug 1, 2004

### Goalie_Ca

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. Aug 1, 2004

### maverick280857

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

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook