A community for students.
Here's the question you clicked on:
 0 viewing
spyros
 3 years ago
integral(sec(x)^3)
spyros
 3 years ago
integral(sec(x)^3)

This Question is Open

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.1\[ \int \sec^3x dx \text{ or } \int \sec (x^3) dx ??\]

spyros
 3 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits(\sec(x)^3dx\]

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.1\[ \sec^3x = \sec^2 \sec x = (1 + \tan^2x) \sec x\]

spyros
 3 years ago
Best ResponseYou've already chosen the best response.0actually( \[\int\limits{\sqrt(1+(x1)^2)dx}\]

spyros
 3 years ago
Best ResponseYou've already chosen the best response.0@experimentX i'll try that one

spyros
 3 years ago
Best ResponseYou've already chosen the best response.0i came to integral(sec(x)^3dx) from integral(sqrt(1+(x1)^2)dx

slaaibak
 3 years ago
Best ResponseYou've already chosen the best response.1\[\int\limits_{}^{} \sec^3(x) = \int\limits_{}^{}\sec x {d \over dx} \tan x = \sec x \tan x  \int\limits \sec (x)\tan^2x \] \[\int\limits \sec^3(x) = \sec x \tan x  \int\limits \sec x (\sec^2(x)  1) \]

slaaibak
 3 years ago
Best ResponseYou've already chosen the best response.1Now take the second part further

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.1int sqrt(1 + (x1)^2) dx = (1/4*(2*x2))*sqrt(2+x^22*x)+(1/2)*arcsinh(x1)

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.1if case of any confusion plugin integration to wolframalpha and click for show steps

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.2Just a little try, not sure if it is correct but hope it helps \[\int sec^3xdx\]\[=\int secx(1+tan^2x)dx\]\[=\int secx+secxtan^2xdx\]\[=\int secxdx+\int secxtan^2xdx\]\[=\int \frac{secx(secx+tanx)}{secx+tanx}dx+\int tanxd(secx)\]\[=\int \frac{1}{secx+tanx}d(secx+tanx)+[secxtanx\int secxd(tanx)]\]\[=\ln secx+tanx+[secxtanx\int secxsec^2xdx] +C\]\[=\ln secx+tanx+[secxtanx\int sec^3xdx] +C\] So, we've got \[\int sec^3xdx=\ln secx+tanx+secxtanx\int sec^3xdx +C\]\[2\int sec^3xdx=\ln secx+tanx+secxtanx +C\]\[\int sec^3xdx=\frac{1}{2}(\ln secx+tanx+secxtanx) +C\]
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.