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anonymous
 one year ago
how do i do this integral?
anonymous
 one year ago
how do i do this integral?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{} \frac{ 1 }{ \sqrt{x}  \sqrt[3]{x} }dx\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and it says hint: substitute….\[u = \sqrt[6]{x}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not sure what i would be doing next? :/

inkyvoyd
 one year ago
Best ResponseYou've already chosen the best response.2did you try it? what does du equal?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3maybe this is an easier form : \(u = \sqrt[6]{x} \implies u^6 = x\) now try expressing \(dx\) in terms of \(du\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, so dx = 6u^5 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh yes, oops :P what am i looking for next? :/

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3pretty sure you meant dx = 6u^5 `du`

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do i need to find any other ones? :/

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3you want to evaluate the given antiderivative

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not sure if I'm doing the right thing? :/

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not sure, wait evaluate the antiderivative? so am i plugging in? :/

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5\[\frac{ dx }{ du }\] is what you want

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, so i get 6u^5 / sqrt x  x^1/3 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so dx = 6u^5 du ? but how do i find du?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1dx = 6u^5 `du` So if you treated du as a variable... how would you isolate it to one side?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1Where did the ve come from....

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hahaha ooh not sure so it is just positive?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so dx is just 1/6u^5 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohhhh okay i see now :) oopsies sorry!! what happens next?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5Ok I feel this is all over the place, so I'm just going to restart

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5\[u^6 = x \implies 6u^5du = dx\] so far so good?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5Now don't start moving things to dx, because that doesn't make much sense, so lets just sub this into our integral now...\[\int\limits \frac{ 6u^5du }{ \sqrt{u^6}\sqrt[3]{u^6} }\] now simplify this, what do you get?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay!! we get sqrt u^6/4 3u^3/4 ? :/

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5I don't know what you did, but just simplify the integrand so we get \[6 \int\limits \frac{ u^5 }{ u^3u^2 }du\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5Can you finish it off from there?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5\[\int\limits \frac{ 6u^5 }{ u^{6/2}u^{6/2} }du \implies 6 \int\limits\limits \frac{ u^5 }{ u^3u^2 }du\] so it's more clear

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hopefully :P would i get this? \[\frac{ u^3 }{ 3 } + \frac{ u^2 }{ 2 } + u + \log(u1) +C \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would this be my solution?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5Yeah, but you have the 6 out there to, so you have to multiply through by 6 and subtitute your original \[u = \sqrt[6]{x}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohhh okay, so i would get this? 2u^3 + 3u^2 + 6u + 6log(u1) + C ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and then wherever there is a u, i just plug that in and whatever i get there will be my final solution?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yay!! thank you!!: )

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5You should put absolute values ln...

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1Can you show how you would simplify the integral, \[6\int \frac{u^5}{u^3u^2}du\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1@iheartfood how did you go from the integral to \(\dfrac{ u^3 }{ 3 } + \dfrac{ u^2 }{ 2 } + u + \log(u1) +C\) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i split them up into different parts!!

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5Long division > +11 trick xd

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1\[\int \frac{u^5}{u^3u^2} du =\int \frac{u^5}{u^2(u1)}du =\int \frac{u^3}{u1}du \]dw:1442987647349:dw \[\int \left(u^2+u+1+\frac{1}{u1}\right)du\]\[=\frac{u^3}{3}+\frac{u^2}{2}+u+\log(u1) +c\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5Yeah perfect! But the original question had a 6 outside, haha but great work!

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.1\[=6\left[ \frac{u^3}{3}+\frac{u^2}{2}+u+\log(u1)+c\right]\] \[=2u^3+3u^2+6u+\log(u1)^6+6c\] this? lol

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5\[=2u^3+3u^2+6u+6\lnu1+c\] looks good

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5Now we just plug our original substitution and we're done

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5The other method is you basically subtract and add 1, then separate the numerator so we have \[6 \int\limits \frac{ u^31+1 }{ u1 }du \implies 6 \int\limits \left( \frac{ u^31 }{ u1 }+\frac{ 1 }{ u1 } \right)du\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5\[(a^3b^3)=(ab)(a^2ab+2b^2)\]...etc

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5Guess I'll show it xD \[6 \int\limits \left( \frac{ (u1)(u^2+u+1) }{ (u1) }+\frac{ 1 }{ u1 } \right)du \implies 6 \int\limits (u^2+u+1+\frac{ 1 }{ u1 }) du\]
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