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

[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!

 

[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

 

[Goalie_Ca]

To clarify, keep integrating by parts until you get your original integral. then move that integral to the other side of the equation and solve :D

 

[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