A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
monroe17
 2 years ago
help step by step?
integral of (2sec^2(x))/(1+tan^2(x))dx
monroe17
 2 years ago
help step by step? integral of (2sec^2(x))/(1+tan^2(x))dx

This Question is Closed

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.0I want to be shown step by step.. explaining..

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.0start using the identity \[1+\tan^2 x= \sec^2 x\]

AnElephant
 2 years ago
Best ResponseYou've already chosen the best response.0you can also do it via substitution: integral of (2sec^2(x))/(1+tan^2(x))dx = 2 (integral of (sec^2(x))/(1+tan^2(x))dx) because 2 is a constant 2 (integral of (sec^2(x))/(1+tan^2(x))dx) ; u=tan(x) du= sec(x)^2 then you're left with 2 (integral of 1/(1+u^2)dx) ; you may notice this is equal to 2arctan(u) substitute tanx back in for u, and you recieve 2arctan(tan(x)) = 2x The most general version of this is 2x+C which is your answer (sorry if the math text is a bit hard to read (I'm new here and really lost lol)
Ask your own question
Ask a QuestionFind 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.