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anonymous
 4 years ago
can someone help me solve an integral?
anonymous
 4 years ago
can someone help me solve an integral?

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1326769120780:dw

Akshay_Budhkar
 4 years ago
Best ResponseYou've already chosen the best response.0the thing that immediately comes to my mind is use the \[\int\limits_{}^{} uvdx\] formula twice

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok in the midst of doing that

Akshay_Budhkar
 4 years ago
Best ResponseYou've already chosen the best response.0but that will be a lengthy business, must have a shorter route

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so what do u suggest?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0cos(x)= Re[e^(i x)] x= e^(ln x) \[\int e^{ln(x)} e^x e^{i x} dx\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\int e^{ln(x)+x+i x} dx\]

Akshay_Budhkar
 4 years ago
Best ResponseYou've already chosen the best response.0Complex numbers!! y didnt i think of that!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0cos(x)= Re[e^(i x)] what is this step?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Using integration by parts three times to solve it isn't that bad either. It would take a while to type out all of the equations, but if you use 1. u=xe^x, dv=cos(x), then 2. u=xe^x, dv=sin(x), then 3. u=e^x, dv=cos(x) over your three stages, you will get the answer of \[\int xe^x\cos x dx = \frac{1}{2}xe^x(\sin x + \cos x)  \frac{1}{2}e^x\sin x + C\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Eh. I would hesitate using complex numbers if you don't know how, you can get yourself into trouble.... using the natural extension of integration by parts to three functions is simple and straightforward, and makes sense already.

Akshay_Budhkar
 4 years ago
Best ResponseYou've already chosen the best response.0@imperialist that will be a bit of lengthy business though, if she knows complex numbers it will be faster

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@Jemurray3, I agree. It would take far longer to explain why you can use complex numbers here (and even longer to understand it!) than 3 applications of integration by parts.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I am just gonna wait to see what myin has to say for herself

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.4First lets evaluate: \[\int\limits_{}^{}e^x \cos(x) dx\] \[=e^x \cos(x)\int\limits_{}^{}e^x(\sin(x)) dx=e^x \cos(x)+\int\limits_{}^{}e^x \sin(x) dx\] \[=e^x \cos(x)+(e^x \sin(x)\int\limits_{}^{}e^x \cos(x) dx)\] So we have \[\int\limits_{}^{}e^x \cos(x) dx=e^x \cos(x)+(e^x \sin(x)\int\limits_{}^{}e^x \cos(x) dx)\] So we shall solve this for: \[\int\limits_{}^{}e^x \cos(x) dx\] So we have \[\int\limits_{}^{}e^x \cos(x) dx=\frac{1}{2}e^x \cos(x)+\frac{1}{2}e^{x}\sin(x)+c_1\] ok now let's look back at \[\int\limits_{}^{} x e^x \cos(x) dx\] Apply integration by parts again! :) \[=(\frac{1}{2}e^x \cos(x)+\frac{1}{2}e^x \sin(x))x\frac{1}{2}\int\limits_{}^{}(e^x \cos(x)+e^x \sin(x)) dx\] So we still need to find \[\int\limits_{}^{}e^x \sin(x) dx\] So we will need integration by parts again \[=e^x \sin(x)\int\limits_{}^{}e^x \cos(x) dx\] \[=e^x \sin(x)(e^x \cos(x)\int\limits_{}^{}e^x (\sin(x)) dx)\] So we need to solve this for: \[\int\limits_{}^{}e^x \sin(x) dx\] \[\int\limits_{}^{}e^x \sin(x) dx=\frac{1}{2} e^x \sin(x)\frac{1}{2}e^x \cos(x)+ c_2\] So we need to put all of this together! lol

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.4\[\int\limits_{}^{}x e^x \cos(x) dx=\frac{1}{2}x e^x \cos(x)+\frac{1}{2}x e^x \sin(x)\frac{1}{2}(\frac{1}{2}e^x \cos(x)+\frac{1}{2}e^x \sin(x)+\] \[\frac{1}{2}e^x \sin(x)\frac{1}{2}e^x \cos(x))+C\] after adding up all the constants I get C lol because the sum of some constants is still constant I think I got every part in there

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Thanks myin but u did it differently then what the others suggested

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I wish I could give you a dozen medals myininaya for typing all of that up! :)

Akshay_Budhkar
 4 years ago
Best ResponseYou've already chosen the best response.0i tell her that for every answer! she is more than cool! :D

Akshay_Budhkar
 4 years ago
Best ResponseYou've already chosen the best response.0just tell ur kids not to trouble me @ myin :P :P

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Thanks myin imperialist and jemurray:D I will have to review th steps now :D

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.4You guys are really sweet! :)

Akshay_Budhkar
 4 years ago
Best ResponseYou've already chosen the best response.0ur kids are sweet too :D

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Oh myin u deserve the medal not me LOL

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.4I don't have kids lol

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.4you have kids not me lol

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Akshay is like1o years younger than you LOL

Akshay_Budhkar
 4 years ago
Best ResponseYou've already chosen the best response.0yea i told her that she doesnt get me! her kidds come to my bakery and dont pay me

Akshay_Budhkar
 4 years ago
Best ResponseYou've already chosen the best response.0LOL junk to be precise

Akshay_Budhkar
 4 years ago
Best ResponseYou've already chosen the best response.0myin is blushing when i told her she has kids :P

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0lol she is dating satellite LOL hehe

Akshay_Budhkar
 4 years ago
Best ResponseYou've already chosen the best response.0satellite is 40 years old!

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.4You guys are crazy. I never met satellite in person.

Akshay_Budhkar
 4 years ago
Best ResponseYou've already chosen the best response.0rld study dont tease :P :P

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yup got loads of work to do. Thanks myin U r awesome

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0LOL dont even have to say that

Akshay_Budhkar
 4 years ago
Best ResponseYou've already chosen the best response.0yea yea~ :P i m so cool :P

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0if u live in my city = cool

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0myin helped me solve it but i know u like integrals. The second I posted it u disappeared LOL Too bad

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0My bad, I'll help on the next one.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ya but now i am doing stupis things. I gotta refer to the tables of integrands and solve accordingly. Soon I will be solving using trig subsitution so i will be back :D
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