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appleduardo Group TitleBest ResponseYou've already chosen the best response.0
\[\ \int\limits_{}^{} \frac{ 2x }{ 2x ^{2}+1 }\]
 one year ago

sanchez9457 Group TitleBest ResponseYou've already chosen the best response.1
Have you learned about USubstitution yet?
 one year ago

appleduardo Group TitleBest ResponseYou've already chosen the best response.0
uhmm nope i dont ! :/
 one year ago

sanchez9457 Group TitleBest ResponseYou've already chosen the best response.1
Hm well i can tell you how to do it using USubstitution but i won't make much sense.
 one year ago

appleduardo Group TitleBest ResponseYou've already chosen the best response.0
i just searched what u substitution means, and i noticed that i cant make use of formulas.. in this case may i use the S du/u = ln u +c? (?)
 one year ago

sanchez9457 Group TitleBest ResponseYou've already chosen the best response.1
well you could set 2x^2 to be your u
 one year ago

sanchez9457 Group TitleBest ResponseYou've already chosen the best response.1
when you derive that you get a simple function you could use.
 one year ago

sanchez9457 Group TitleBest ResponseYou've already chosen the best response.1
sorry i meant set your u to be 2x^2 + 1
 one year ago

sanchez9457 Group TitleBest ResponseYou've already chosen the best response.1
\[ u = 2x^2 +1\] \[du = 4xdx\]
 one year ago

sanchez9457 Group TitleBest ResponseYou've already chosen the best response.1
divide the du function across by 2:
 one year ago

sanchez9457 Group TitleBest ResponseYou've already chosen the best response.1
\[\frac{ du }{ 2 } = 2xdx\]
 one year ago

sanchez9457 Group TitleBest ResponseYou've already chosen the best response.1
Then your new integral would be:
 one year ago

sanchez9457 Group TitleBest ResponseYou've already chosen the best response.1
\[\frac{ 1 }{ 2 }\int\limits_{?}^{?} \frac{ 1 }{ u } du\]
 one year ago

sanchez9457 Group TitleBest ResponseYou've already chosen the best response.1
if you integrate that you get: \[\frac{ 1 }{ 2 }\left[ logu \right] + C\]
 one year ago

sanchez9457 Group TitleBest ResponseYou've already chosen the best response.1
then replace that u with the equation it was set to:
 one year ago

sanchez9457 Group TitleBest ResponseYou've already chosen the best response.1
\[= \frac{ 1 }{ 2 } \log(2x^2 +1)\]
 one year ago

sanchez9457 Group TitleBest ResponseYou've already chosen the best response.1
And there you have your answer
 one year ago

appleduardo Group TitleBest ResponseYou've already chosen the best response.0
oh my gosh thank you so much ! . :D but i have a question, why did u divided du by 2?
 one year ago

sanchez9457 Group TitleBest ResponseYou've already chosen the best response.1
i divided du by 2 so it can look like something i already had. I could have done it withoug dividing by 2 but i like to simplify things.
 one year ago

sanchez9457 Group TitleBest ResponseYou've already chosen the best response.1
by somthign i had already i meant 2x. from the original integral.
 one year ago
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