anonymous
  • anonymous
integrate:
Mathematics
jamiebookeater
  • jamiebookeater
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
|dw:1352245389039:dw|
anonymous
  • anonymous
i really dont have an idea...
anonymous
  • anonymous
|dw:1352246169490:dw|

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
anonymous
  • anonymous
Neither do I.. :( Let u=x+4 du = dx => x+2 = u-2 ; x = u-4 \[\int (\frac{x+2}{x+4})^2 e^x dx = \int (\frac{u-2}{u})^2 e^{u-4}du = \int\frac{u^2-4u+4}{u^2}e^{u-4}du\]\[=\int (e^{u-4}-\frac{4e^{u-4}}{u}+\frac{4e^{u-4}}{u^2})du\] I'm sure @hartnn has a better idea!!
hartnn
  • hartnn
can u find derivative of x/(x+4) ??
anonymous
  • anonymous
yes...wait...but why x / x+4?
hartnn
  • hartnn
find its derivative, u'll come to know.....
anonymous
  • anonymous
|dw:1352246668426:dw|
hartnn
  • hartnn
wait i think i made a mistake....
hartnn
  • hartnn
u'll need integration by parts. but that becomes very messy...
hartnn
  • hartnn
i just realized that x/x+4 + d/dx (x/x+4) = [(x+2)/(x+4)]^2
hartnn
  • hartnn
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
hartnn
  • hartnn
i don't know how to explain that ....
anonymous
  • anonymous
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
anonymous
  • anonymous
yes..that's im about to type lol thanks! @hartnn @RolyPoly
hartnn
  • hartnn
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.....
hartnn
  • hartnn
comes with practice, i guess...

Looking for something else?

Not the answer you are looking for? Search for more explanations.