1. integration by parts

i know this probably seems really trivial, but in college calc we basically have to teach ourselves.. and i don't understand where i'm going wrong >.<

the problem is, integral (e^x)(cosx)dx

so i figured this is something you'd go about by using parts

u= e^x v= sinx
du= e^xdx dv= cosxdx

then you get e^x(sinx)- integral e^x(sinx)

doing parts again.. u= sin x v= e^x
du= cosxdx dv= e^xdx

and it seems like i'm going to get e^x(sinx)-e^x(sinx) * integral (e^x)(cosx)dx which is where i started..

this is a mistake that i often make in parts.. please help? i need to be able to understand/explain what i did

2. Originally Posted by buttonbear
i know this probably seems really trivial, but in college calc we basically have to teach ourselves.. and i don't understand where i'm going wrong >.<

the problem is, integral (e^x)(cosx)dx

so i figured this is something you'd go about by using parts

u= e^x v= sinx
du= e^xdx dv= cosxdx

then you get e^x(sinx)- integral e^x(sinx)

doing parts again.. u= sin x v= e^x
du= cosxdx dv= e^xdx

and it seems like i'm going to get e^x(sinx)-e^x(sinx) * integral (e^x)(cosx)dx which is where i started..

this is a mistake that i often make in parts.. please help? i need to be able to understand/explain what i did
I don't think integration by parts is the way to go for this. As you say, it doesn't make it any easier.

3. okay..

can you give me a hint?

4. Originally Posted by buttonbear
okay..

can you give me a hint?
Oh I'd love to, I'm thinking about it myself

5. Originally Posted by buttonbear
i know this probably seems really trivial, but in college calc we basically have to teach ourselves.. and i don't understand where i'm going wrong >.<

the problem is, integral (e^x)(cosx)dx

so i figured this is something you'd go about by using parts

u= e^x v= sinx
du= e^xdx dv= cosxdx

then you get e^x(sinx)- integral e^x(sinx)

doing parts again.. u= sin x v= e^x
du= cosxdx dv= e^xdx

and it seems like i'm going to get e^x(sinx)-e^x(sinx) * integral (e^x)(cosx)dx which is where i started..

this is a mistake that i often make in parts.. please help? i need to be able to understand/explain what i did
$\displaystyle \int e^x \cos{x} \, dx$

$\displaystyle u = \cos{x}$ ... $\displaystyle dv = e^x dx$

$\displaystyle du = -\sin{x} \, dx$ ... $\displaystyle v = e^x$

$\displaystyle \int e^x \cos{x} \, dx = e^x\cos{x} + \int e^x \sin{x} \, dx$

$\displaystyle u = \sin{x}$ ... $\displaystyle dv = e^x \, dx$

$\displaystyle du = \cos{x} \, dx$ ... $\displaystyle v = e^x$

$\displaystyle \int e^x \cos{x} \, dx = e^x\cos{x} + e^x \sin{x} - \int e^x \cos{x} \, dx$

$\displaystyle 2\int e^x \cos{x} \, dx = e^x\cos{x} + e^x \sin{x}$

$\displaystyle \int e^x \cos{x} \, dx = \frac{e^x(\cos{x} + \sin{x})}{2} + C$

6. thanks a lot for your help

so, basically i was just doing the substitutions backwards?

i guess i should just try to be more persistent and not give up so quickly..