A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
integrate (1/(x^2+8x +25 )^0.5)
anonymous
 4 years ago
integrate (1/(x^2+8x +25 )^0.5)

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0This is a hard one x^2+8x+25=(x+4)^2+9 so use sub u=x+4 du=dx New integral: 1/(u^2+9)^0.5

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0hmmm ya i also reached at this point but what after this?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0thinking of the next substitution, maybe some trig function

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0hmm yes i think that would be tan but how and why

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I know! Recall that tan^2(x)+1=sec^2(x)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so we need to make 9tan^2(x) from u to get 9(tan^2(x)+1)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0let u=3tan(z) du=3sec^2(z) dz

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0So the integral will be: 3sec^2(z)/3sec(z)=sec(z)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0What the integral of secz? log(tanz+secz) (just looked it up)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0we have u=3tanz expressing z=tan^1(u/3)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0thanks man.. well pretty much hit the answer but can u explain this 1 step let u=3tan(z) du=3sec^2(z) dz.. why we suppose 3 tan(z) why not just tan

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0because if it is 3tan than (3tan)^2=9tan^2(x) so we can factor out 9 to get 9(tan^2(x)+1)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ohh so just that was the reason to put 3?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Hope it helped, now you just need to plug back the z and u to get x

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0do you know about hyperbolic functions ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0and this is a elementary problem no need to think hard on this one

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0e^x+e^x/2 how would that help?

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.0\[\frac{d}{dx}\operatorname{arsinh}(x) =\frac{1}{\sqrt{x^{2}+1}}\]
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.