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terenzreignz Group TitleBest ResponseYou've already chosen the best response.0
\[\huge \int \frac{x^4}{1x}dx\]
 one year ago

appleduardo Group TitleBest ResponseYou've already chosen the best response.0
yep, but how can I solve it?
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.0
It's actually quite easy, but incredibly tedious. Use usubstitution. When in doubt, attempt to let u = the denominator of a rational expression... chances are, that's the one...
 one year ago

appleduardo Group TitleBest ResponseYou've already chosen the best response.0
what u mean with rational expression?
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.0
Fraction. Fancy word for fraction.
 one year ago

appleduardo Group TitleBest ResponseYou've already chosen the best response.0
so u say that Ive to use u=x^4, du/dx=4x^3 so dx=du/4x^3 then: \[\frac{ u }{ 1x }\frac{ du }{ 4x^3 }\]
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.0
Unfortunately not that simple. u was in your denominator, wasn't it?
 one year ago

appleduardo Group TitleBest ResponseYou've already chosen the best response.0
oh yeep ure right, so its: u=(1x) du/dx= 1 dx= du/1 and then: \[\int\limits_{}^{}\frac{ x^4 }{ u}*\frac{ du }{ 1 } = \int\limits_{}^{}\frac{ x^4 }{ u}*du\]
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.0
Okay, much better. But you cannot solve this integral without expressing \(x^4\) in terms of u.
 one year ago

appleduardo Group TitleBest ResponseYou've already chosen the best response.0
so.. what can I do??
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.0
Well \[\large u = 1x\] \[\large x = 1u\] \[\huge x^4 = (1u)^4\]
 one year ago

appleduardo Group TitleBest ResponseYou've already chosen the best response.0
wow! so uhm,, what do I have to do now?
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.0
Expand.
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.0
\[\large (1u)^4 = u^4 4u^3 +6u^2 4u +1\]
 one year ago

appleduardo Group TitleBest ResponseYou've already chosen the best response.0
so now I have: \[\frac{ x^4 }{ u^4  4u^3 + 6u^2  4u + 1 }\] but at this point is u still = to (1x) ? sorry if this sounds silly or so, but I got a little confused when u got (1u)^4
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.0
No... remember, you started with \[\huge \int \frac{x^4}{1x}dx\]And you let u = 1x, work from there, and substitute.
 one year ago

appleduardo Group TitleBest ResponseYou've already chosen the best response.0
mm so what I = to "u" then? :/
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.0
Shun being spoonfed, @appleduardo ... :P \[\large u = 1x\]\[\large du = dx\]\[\large dx = du\]\[\large x = 1u\]\[\large x^4=(1u)^4\]
 one year ago
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