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

sanchez9457
 2 years ago
Best ResponseYou've already chosen the best response.1Have you learned about USubstitution yet?

appleduardo
 2 years ago
Best ResponseYou've already chosen the best response.0uhmm nope i dont ! :/

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

appleduardo
 2 years ago
Best ResponseYou've already chosen the best response.0i 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? (?)

sanchez9457
 2 years ago
Best ResponseYou've already chosen the best response.1well you could set 2x^2 to be your u

sanchez9457
 2 years ago
Best ResponseYou've already chosen the best response.1when you derive that you get a simple function you could use.

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

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

sanchez9457
 2 years ago
Best ResponseYou've already chosen the best response.1divide the du function across by 2:

sanchez9457
 2 years ago
Best ResponseYou've already chosen the best response.1\[\frac{ du }{ 2 } = 2xdx\]

sanchez9457
 2 years ago
Best ResponseYou've already chosen the best response.1Then your new integral would be:

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

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

sanchez9457
 2 years ago
Best ResponseYou've already chosen the best response.1then replace that u with the equation it was set to:

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

sanchez9457
 2 years ago
Best ResponseYou've already chosen the best response.1And there you have your answer

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

sanchez9457
 2 years ago
Best ResponseYou've already chosen the best response.1i 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.

sanchez9457
 2 years ago
Best ResponseYou've already chosen the best response.1by somthign i had already i meant 2x. from the original integral.
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