A community for students.
Here's the question you clicked on:
 0 viewing
suju101
 3 years ago
integrate sin(tan^1x)/(1+x^2). please help with the steps
suju101
 3 years ago
integrate sin(tan^1x)/(1+x^2). please help with the steps

This Question is Closed

imperialist
 3 years ago
Best ResponseYou've already chosen the best response.3Set u=arctan(x), so that du= 1/(1+x^2). Thus, using this usubstitution, the integral is equivalent to the integral of sin(u). Since the integral of sin(u) is cos(u)+C, the final answer is just \[\sin (\tan^{1} (x))+C\] Note also that sin(arctan(x)) is the same as \[x/\sqrt{x^2+1}\] So that function plus your constant of integration is also a correct solution.

imperialist
 3 years ago
Best ResponseYou've already chosen the best response.3Sorry, it should be \[\cos (\tan^{1} (x))+C\]

imperialist
 3 years ago
Best ResponseYou've already chosen the best response.3Also, that means that the alternate answer is instead \[1/\sqrt{x^2+1} + C\]
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.