A community for students.
Here's the question you clicked on:
 0 viewing
shubhamsrg
 3 years ago
integral [ log( sqrt(1+x) + sqrt(1x) ) dx] from x=0 to 1
shubhamsrg
 3 years ago
integral [ log( sqrt(1+x) + sqrt(1x) ) dx] from x=0 to 1

This Question is Closed

lgbasallote
 3 years ago
Best ResponseYou've already chosen the best response.0\[\huge \int \limits_0^1 \log (\sqrt{1 + x} + \sqrt{1 x})\] ???

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0yep.. and a dx there,,ofcorse..

vikrantg4
 3 years ago
Best ResponseYou've already chosen the best response.0ah.. leave the typos.. concentrate on question. lol

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2simple substitution of x=cos 2t

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0then our dx = 2sin 2t dt.. dont you think that will create a problem ? altough the sq. roots will be eliminated..

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0how'd you get that ? what i got was inside the integral (something) + log( cos t + sin t ) sin 2t dt are you missing the log there buddy ?

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.0man this is interesting

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.0let\[t=\ln(\sqrt{1+x}+\sqrt{1x})\]

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2is there a standard formula for: \[\int\limits_{}^{}\ln(1+\sqrt{1x^2})\] if yes,then this is so simple!

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2\[=(1/2)\int\limits \limits_0^1 \log (\sqrt{1 + x} + \sqrt{1 x})^2 dx\] \[=(1/2)\int\limits \limits_0^1 \log (2+2\sqrt{1x^2})^2 dx\] \[=(1/2)\int\limits \limits_0^1 \ln 2+\ln (1+\sqrt{1x^2})^2 dx\]

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2\[=(1/2)\int\limits\limits\limits \limits_0^1 \ln 2+\int\limits\limits\limits \limits_0^1\ln (1+\sqrt{1x^2}) dx\]

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.0\[\ln(1+\sqrt{1x^2})=\text{sech}^{1}x+\ln x\]this is hard to get o.O

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=%5Cint+%5Cln+%281%2B%5Csqrt%7B1x%5E2%7D%29+dx

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2http://www.wolframalpha.com/input/?i=integral+of+ln%281%2Bsqrt%7B1x%5E2%7D%29&dataset=

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2lol,i did same exact thing :P

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2i guess,thats integration by parts........???

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0bingo,,got it by parts! @hartnn thanks a lot!
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.