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

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

terenzreignzBest 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

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

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

appleduardoBest 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

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

appleduardoBest 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

terenzreignzBest 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

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

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

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

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

appleduardoBest 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

terenzreignzBest 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

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

terenzreignzBest 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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