• anonymous
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(1-x^2)^(-1/2)
  • jamiebookeater
See more answers at
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly


Get your free account and access expert answers to this
and thousands of other questions

  • anonymous
First of all, for the sake of simplicity, lets pretend that antiderivatives are the same as integrals (they pretty much are). Also, when I say\[\int\limits_{}{} \frac {2x+5}{\sqrt{1-x^2}}\] I mean "take the antiderivate of 2x+5(1-x^2)^(-1/2). So the first thing we notice is that we could rewrite the problem to \[\int\limits_ {}{} \frac {1}{\sqrt{1-x^2}} * 2x+5\] If we look on the left hand side, we notice that we have the term \[\int\limits_ {}{} \frac {1}{1-x^2}\] Which is the derivative of inverse sine \[\sin^{-1}\]
  • anonymous
EDIT. I totally mean to have a square root sign under the 1-x^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. \[\int\limits\limits\limits {}{} \frac{1}{\sqrt{1-x^2}} (2x+5)\] The 1-x^2 is the "driving function," or if you learn u-substitution 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 U-substitution (or read about it yourself!)

Looking for something else?

Not the answer you are looking for? Search for more explanations.