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

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

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

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

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

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

slaaibak
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.0what is arctan e^1???

slaaibak
 one year 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
 one year 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
 one year 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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