Method for integrating product of two fuctions that drive forever?

[Techie333]

I am in differential equations!!!!! This is scary!!! I can't remember how the method for integrating the product of two fuctions that derive forever, for example (e^-x)(sinx)......

 

[DrPizza]

integration by parts....
(u dv substitutions)
integral of udv = uv - integral of v du

 

[DrPizza]

I'm not going to bother attempting the one you have there (it's fairly easy though)... but it looks like one that you'd do an integration by parts twice on... and you end up with the original integral again (only negative), sort of like
integral = blah blah blah - integral.
move the integral on the right to the left so it's
2 integral = blah blah blah
then divide by 2 and you have the answer

 

[Techie333]

Originally posted by: DrPizza
I'm not going to bother attempting the one you have there... but it looks like one that you'd do an integration by parts twice on... and you end up with the original integral again (only negative), sort of like
integral = blah blah blah - integral.
move the integral on the right to the left so it's
2 integral = blah blah blah
then divide by 2 and you have the answer

OH YEA!!! THANKS!!! I REMEMBER NOW!!

 

[DrPizza]

such wonderful mathematical terms - "blah blah blah"

the easier way to do that integral is with mathematica or maple (or some other integrating program)

Or, you could look it up in a table of integrals found in the front and back of nearly every calculus book there is...

 

[Techie333]

Originally posted by: DrPizza
such wonderful mathematical terms - "blah blah blah"

the easier way to do that integral is with mathematica or maple (or some other integrating program)

Or, you could look it up in a table of integrals found in the front and back of nearly every calculus book there is...

BTW, that stuff isn't in the DQ book because you are so high up in the math chain, they expect you to know it.....no integral table or anything.....

 

[DrPizza]

Yeah, but if you're taking diff eq's, you ought to have a calculus book sitting on a shelf somewhere...