A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
integrate 1/sec^2xtanx
anonymous
 3 years ago
integrate 1/sec^2xtanx

This Question is Closed

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{}^{}\frac{ 1 }{ \sec^2xtanx }dx\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{?}^{?} \frac{ \cos x }{ \sec x \tan x }=\int\limits_{?}^{?} \frac{ 1 }{ \sec x \tan x }* \cos x\] you can use integration by parts now, and sec x tan x is differentiation of sec x

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0umm how did you get that first integral, sorry I'm confused

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0or would I just turn the sec^2x into (1tan^2x)?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{}^{}cotxcos^2xdx\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0is that basically the same thing?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0sorry just needed to vent

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I'm starting to wonder if maybe I did the original problem wrong to even get to this scenario.... the original integral was \[\int\limits_{}^{}\frac{ 188 }{ x^2\sqrt{16x^281} }dx\]

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.0int 1/sec^2xtanx dx = int cos^2 x cosx/sinx dx = int (1sin^2 x)cosx/sinx dx = int cosx/sinx dx  int sinxcosx dx = int cosx/sinx dx  int 1/2*sin2x dx case I : int cosx/sinx dx int by usub let u=sinx > du = cosx dx so, int cosx/sinx dx = int du/u = ln(u) = ln(sinx) case II :  int 1/2*sin2x dx = (1/4 cos2x) = 1/4 cos2x so, the total = ln(sinx) + 1/4 cos2x

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0from there I got this: \[47\int\limits_{}^{}\frac{ 1 }{ x^2\sqrt{x^2(\frac{ 9 }{ 4 })^2} }\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so then I did \[x=\frac{ 9 }{ 4 }\sec\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0that should be sec theta

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0and from there I got \[47\int\limits_{}^{}\frac{ 1 }{ (\frac{ 9 }{ 4 })^2\sec^2\theta(\frac{ 9 }{ 4 })\tan \theta }d \theta \]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0somebody stop me if I'm screwing up lol

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.0i have done it above @stottrupbailey happy valentine's day , hahaha

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so then I get \[47 (\frac{ 4 }{ 9 })^3\int\limits_{}^{}\frac{ 1 }{ \sec^2\theta \tan \theta }d \theta\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0And thus the current dilemma, the integral of sec^2tan

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I'm confused by RadEn's explanation, can someone maybe explain what they did there? I got lost when he broke it up into subtracting two integrals...

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.0sorry, i didnt see the original problem.. i just see the first posting

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.0well, ur original problems is int ( 188/(x^2sqrt(16x^281)) dx in the frist step u have right let x = 9/4 secθ > x^2=9/16 sec^2 x dx = 9/4 secθtanθ dθ and for sqrt(16x^281), it can be sqrt(81sec^2 θ 81) = sqrt(81(sec^2 θ  1) = 9sqrt(tan^2 θ) = 9tanθ so, ur integral can be : dw:1360827737581:dw

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.0from the equation : x = 9/4 secθ or secθ = 4x/9, reprsented in the figure : dw:1360828428409:dw

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.0thus, the result is = 752/9 sinθ + c = 752/9 * sqrt(16x^2  81)/(4x) + c
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.