Integral

[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 untill 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