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KarlaKalurky Group TitleBest ResponseYou've already chosen the best response.0
dw:1352245389039:dw
 one year ago

KarlaKalurky Group TitleBest ResponseYou've already chosen the best response.0
i really dont have an idea...
 one year ago

KarlaKalurky Group TitleBest ResponseYou've already chosen the best response.0
dw:1352246169490:dw
 one year ago

KarlaKalurky Group TitleBest ResponseYou've already chosen the best response.0
@RolyPoly
 one year ago

RolyPoly Group TitleBest ResponseYou've already chosen the best response.1
Neither do I.. :( Let u=x+4 du = dx => x+2 = u2 ; x = u4 \[\int (\frac{x+2}{x+4})^2 e^x dx = \int (\frac{u2}{u})^2 e^{u4}du = \int\frac{u^24u+4}{u^2}e^{u4}du\]\[=\int (e^{u4}\frac{4e^{u4}}{u}+\frac{4e^{u4}}{u^2})du\] I'm sure @hartnn has a better idea!!
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
can u find derivative of x/(x+4) ??
 one year ago

KarlaKalurky Group TitleBest ResponseYou've already chosen the best response.0
yes...wait...but why x / x+4?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
find its derivative, u'll come to know.....
 one year ago

KarlaKalurky Group TitleBest ResponseYou've already chosen the best response.0
dw:1352246668426:dw
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
wait i think i made a mistake....
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
u'll need integration by parts. but that becomes very messy...
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
i just realized that x/x+4 + d/dx (x/x+4) = [(x+2)/(x+4)]^2
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
then using this : \(\\ \huge \color{red}{\int e^x[f(x)+f’(x)]dx=e^xf(x)+c} \\\) i got the integral as (xe^x)/(x+4) + c
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
i don't know how to explain that ....
 one year ago

RolyPoly Group TitleBest ResponseYou've already chosen the best response.1
Reverse: \[\frac{d}{dx} e^x f(x)+C= e^xf(x)+e^xf'(x)=e^x(f(x)+f'(x))\]So, \[\int e^x(f(x)+f'(x)) = e^xf(x)+C\] And the question, Consider f(x) = x/x+4 f'(x) = 4/(x+4) f(x) + f'(x) = [(x+2)/(x+4)]^2 So, \[\int [\frac{(x+2)}{(x+4)}]^2e^xdx = \int e^x(\frac{x}{x+4}+\frac{4}{(x+4)^2})dx=e^x(\frac{x}{x+4})+C\] Hail @hartnn
 one year ago

KarlaKalurky Group TitleBest ResponseYou've already chosen the best response.0
yes..that's im about to type lol thanks! @hartnn @RolyPoly
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
i meant i can't explain how we can think of f(x) as x/(x+4) all other steps are just use of formula.....
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
comes with practice, i guess...
 one year ago
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