anonymous
  • anonymous
Integral 1/(sqrt(1+e^(2x))) dx
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
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.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
|dw:1371414476132:dw|
hartnn
  • hartnn
i was thinking of this, |dw:1371414628997:dw| multiplying and dividing by e^(-x) would work on paper to see whether it works...
anonymous
  • anonymous
from what i saw in the solution, it looks like they multiplied and divided by e^x, but i thought we couldnt do that? we can only multioply by a constant

Looking for something else?

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

More answers

hartnn
  • hartnn
we CAN multiply and divide by a function too, like e^x or e^(-x) ...
anonymous
  • anonymous
we can do that??!!! I though it was only by a constant.
anonymous
  • anonymous
if we can multiply and divide by a function, then the integral becomes really easy. Thanks. So i can also multipy and divide by x??
hartnn
  • hartnn
why you want to do that ? and now i think, substituting , u = 1+e^(2x) would beeasier.
anonymous
  • anonymous
i mean, not for this integral, but lets say for a different integral, i could possibly divdie and multiply by x?
hartnn
  • hartnn
if that makes the finding the integral easier, then YES, you can do that
anonymous
  • anonymous
Okay, thank you.
anonymous
  • anonymous
:)
hartnn
  • hartnn
welcome ^_^
anonymous
  • anonymous
Another way: If you've learned trigonometric substitutions, you could rewrite the integral first using \[u=e^x~\Rightarrow~du=e^x~dx\\ ~~~~~~~~~~~~~~~\frac{du}{u}=dx\] \[\int\frac{dx}{\sqrt{1+e^{2x}}}~\Rightarrow~\int\frac{du}{u\sqrt{1+u^2}}\] Then use \(u=\tan t~\Rightarrow~du=\sec^2t~dt\).

Looking for something else?

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