A community for students.
Here's the question you clicked on:
 0 viewing
Study23
 2 years ago
Find the most general antiderivative of the following function (note I have NOT learned about integrals yet). I'm confused about the chain rule and the antiderivative. The function: 2x+5(1x^2)^(1/2)
Study23
 2 years ago
Find the most general antiderivative of the following function (note I have NOT learned about integrals yet). I'm confused about the chain rule and the antiderivative. The function: 2x+5(1x^2)^(1/2)

This Question is Closed

Argonx16
 2 years ago
Best ResponseYou've already chosen the best response.1First of all, for the sake of simplicity, lets pretend that antiderivatives are the same as integrals (they pretty much are). Also, when I say\[\int\limits_{}{} \frac {2x+5}{\sqrt{1x^2}}\] I mean "take the antiderivate of 2x+5(1x^2)^(1/2). So the first thing we notice is that we could rewrite the problem to \[\int\limits_ {}{} \frac {1}{\sqrt{1x^2}} * 2x+5\] If we look on the left hand side, we notice that we have the term \[\int\limits_ {}{} \frac {1}{1x^2}\] Which is the derivative of inverse sine \[\sin^{1}\]

Argonx16
 2 years ago
Best ResponseYou've already chosen the best response.1EDIT. I totally mean to have a square root sign under the 1x^2 up there. My bad. So from that, we can conclude that inverse sine will have a part in this integral (antiderivative). So now that we know that inverse sine is part of the question, lets work through the integral again. \[\int\limits\limits\limits {}{} \frac{1}{\sqrt{1x^2}} (2x+5)\] The 1x^2 is the "driving function," or if you learn usubstitution later, the "U," meaning that if the "driving function/U" is responsible for the (2x+5) term per the chain rule. If this doesn't make any sense, just wait until you learn Usubstitution (or read about it yourself!)
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.