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jotopia34
 2 years ago
HELP!!! How do you integrate e^x/1+e^2x*dx
jotopia34
 2 years ago
HELP!!! How do you integrate e^x/1+e^2x*dx

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slaaibak
 2 years ago
Best ResponseYou've already chosen the best response.1can you type it using latex please (the equation tool)?

jotopia34
 2 years ago
Best ResponseYou've already chosen the best response.0Im so sorry I don't know what latex is?

jotopia34
 2 years ago
Best ResponseYou've already chosen the best response.0I typed it into Wolfram before, and got the final answer, but I dont know the steps in between

slaaibak
 2 years ago
Best ResponseYou've already chosen the best response.1Using that equation thing at the bottom. \[\int{e^x \over {1 + e^{2x}}} dx\] does it look like that?

jotopia34
 2 years ago
Best ResponseYou've already chosen the best response.0Oh, I see the equation tool, sorry

slaaibak
 2 years ago
Best ResponseYou've already chosen the best response.1e^x = u du = e^x dx u^2 = e^2x \[\int\limits {1 \over 1 + u^2} du\] now letting u = tan k du = sec^2 k dk so it becomes: \[\int\limits {\sec^2 k \over 1 + \tan^2k} dk\] and that equals (because sec^2 k = tan^2 k + 1) \[\int\limits {\sec^2 k \over \sec^2 k} dk = k + C\] but u = tan k k = arctan u so it's arctan u + C but u = e^x so it's arctan e^x + C you could have directly made the substitution e^x = tan u, but this makes one understand it better

jotopia34
 2 years ago
Best ResponseYou've already chosen the best response.0thanks soooo much, let me have a minute to digest it now.... lol

jotopia34
 2 years ago
Best ResponseYou've already chosen the best response.0I don't understand this part: u^2 = e^2x

jotopia34
 2 years ago
Best ResponseYou've already chosen the best response.0Last question, now how to I evaluate it from 0 to 1?....:(

slaaibak
 2 years ago
Best ResponseYou've already chosen the best response.1Since you know the anti derivative, let's call it F, is F(x) = arctan e^x + C, you simply need to evaluate F(1)  F(0) but because you are subtracting the two functions, you don't have to work with the C, because C  C = 0 So it's arctan(e^1)  arctan(e^0) = arctan(e)  arctan(1)

jotopia34
 2 years ago
Best ResponseYou've already chosen the best response.0what is arctan e^1???

slaaibak
 2 years ago
Best ResponseYou've already chosen the best response.1haha, unfortunately my maths isn't that advanced yet :( but use your calculator to evaluate it.

jotopia34
 2 years ago
Best ResponseYou've already chosen the best response.0okay, I think I may be able to leave the answer at that since their are no calculators on the quiz

slaaibak
 2 years ago
Best ResponseYou've already chosen the best response.1oh, yes. Just leave it in this format: \[\arctan (e)  \arctan (1)\] Do you understand all the steps? I'll elaborate if there is anything that's poorly explained.
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