Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Open

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

spyrosBest ResponseYou've already chosen the best response.0
\[\int\limits(\sec(x)^3dx\]
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
former or latter??
 one year ago

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

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

spyrosBest ResponseYou've already chosen the best response.0
@experimentX i'll try that one
 one year ago

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

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

slaaibakBest ResponseYou've already chosen the best response.1
Now take the second part further
 one year ago

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

experimentXBest ResponseYou've already chosen the best response.1
if case of any confusion plugin integration to wolframalpha and click for show steps
 one year ago

CallistoBest ResponseYou've already chosen the best response.2
Just 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 \[\int sec^3xdx=\ln secx+tanx+secxtanx\int sec^3xdx +C\]\[2\int sec^3xdx=\ln secx+tanx+secxtanx +C\]\[\int sec^3xdx=\frac{1}{2}(\ln secx+tanx+secxtanx) +C\]
 one year ago
See more questions >>>
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.