int by parts(almost finished)

**saiyanmx89** · February 22nd 2009, 03:37 PM

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...

**GaloisTheory1** · February 22nd 2009, 03:50 PM

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

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

**saiyanmx89** · February 22nd 2009, 03:54 PM

where did you get 5e^x from? that's where I get lost....

**skeeter** · February 22nd 2009, 03:58 PM

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

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

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