A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
integrate:
anonymous
 4 years ago
integrate:

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1352245389039:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i really dont have an idea...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1352246169490:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Neither 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!!

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes...wait...but why x / x+4?

hartnn
 4 years ago
Best ResponseYou've already chosen the best response.1find its derivative, u'll come to know.....

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1352246668426:dw

hartnn
 4 years ago
Best ResponseYou've already chosen the best response.1wait i think i made a mistake....

hartnn
 4 years ago
Best ResponseYou've already chosen the best response.1u'll need integration by parts. but that becomes very messy...

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

hartnn
 4 years ago
Best ResponseYou've already chosen the best response.1then 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
 4 years ago
Best ResponseYou've already chosen the best response.1i don't know how to explain that ....

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Reverse: \[\frac{d}{dx} e^x f(x)+C= e^xf(x)+e^xf'(x)=e^x(f(x)+f'(x))\]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
 4 years ago
Best ResponseYou've already chosen the best response.0yes..that's im about to type lol thanks! @hartnn @RolyPoly

hartnn
 4 years ago
Best ResponseYou've already chosen the best response.1i 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
 4 years ago
Best ResponseYou've already chosen the best response.1comes with practice, i guess...
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.