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appleduardo
 3 years ago
whats the integral for x^4 / (1x) ??
appleduardo
 3 years ago
whats the integral for x^4 / (1x) ??

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terenzreignz
 3 years ago
Best ResponseYou've already chosen the best response.0\[\huge \int \frac{x^4}{1x}dx\]

appleduardo
 3 years ago
Best ResponseYou've already chosen the best response.0yep, but how can I solve it?

terenzreignz
 3 years ago
Best ResponseYou've already chosen the best response.0It'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...

appleduardo
 3 years ago
Best ResponseYou've already chosen the best response.0what u mean with rational expression?

terenzreignz
 3 years ago
Best ResponseYou've already chosen the best response.0Fraction. Fancy word for fraction.

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

terenzreignz
 3 years ago
Best ResponseYou've already chosen the best response.0Unfortunately not that simple. u was in your denominator, wasn't it?

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

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

appleduardo
 3 years ago
Best ResponseYou've already chosen the best response.0so.. what can I do??

terenzreignz
 3 years ago
Best ResponseYou've already chosen the best response.0Well \[\large u = 1x\] \[\large x = 1u\] \[\huge x^4 = (1u)^4\]

appleduardo
 3 years ago
Best ResponseYou've already chosen the best response.0wow! so uhm,, what do I have to do now?

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

appleduardo
 3 years ago
Best ResponseYou've already chosen the best response.0so 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

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

appleduardo
 3 years ago
Best ResponseYou've already chosen the best response.0mm so what I = to "u" then? :/

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