# int by parts(almost finished)

• Feb 22nd 2009, 04:37 PM
saiyanmx89
int by parts(almost finished)
original problem:
$\int e^xcos(2x)dx$

I've used int. by parts twice so far and I have this:
$e^xcos(2x) + 2e^xsin(2x) - 4\int e^xcos(2x)dx$

Where do I go from here? I'm lost...
• Feb 22nd 2009, 04:50 PM
GaloisTheory1
Quote:

Originally Posted by saiyanmx89
original problem:
$\int e^xcos(2x)dx$

I've used int. by parts twice so far and I have this:
$e^xcos(2x) + 2e^xsin(2x) - 4\int e^xcos(2x)dx$

Where do I go from here? I'm lost...

$\int e^xcos(2x)dx= e^xcos(2x) + 2e^xsin(2x) - 4\int e^xcos(2x)dx$

so

$\int 5e^xcos(2x)dx= e^xcos(2x) + 2e^xsin(2x)$

so

$\int e^xcos(2x)dx= \frac{e^xcos(2x) + 2e^xsin(2x)}{5}$
• Feb 22nd 2009, 04:54 PM
saiyanmx89
where did you get 5e^x from? that's where I get lost....
• Feb 22nd 2009, 04:58 PM
skeeter
$\textcolor{red}{\int e^xcos(2x)dx}= e^xcos(2x) + 2e^xsin(2x) \textcolor{red}{- 4\int e^xcos(2x)dx}$

note the like terms ... now move $\textcolor{red}{- 4\int e^xcos(2x)dx}$ to the left side and combine.