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Jonask
 one year ago
Best ResponseYou've already chosen the best response.1\[\color{blue}{\huge\int_0^1\sqrt[3]{1x^7}\sqrt[7]{1x^3}dx}\]

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.0\[\color{blue}{\int_0^1\sqrt[3]{1x^7}dx\int\sqrt[7]{1x^3}dx}\]

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1yes but when i do that it still seems ugly

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.0do one half at a time

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1i shud make a u sub \[u=1x^7\]

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1\[u=1x^7\] \[\int\frac{u^{1/3}}{7x^6}du\]

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1\[\int\frac{u^{1/3}}{7(1u)^{1/7}}\]

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.0maybe that method isn't going to work

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1http://www.wolframalpha.com/input/?i=integral+%281x%5E7%29%5E%7B1%2F3%7D%281x%5E3%29%5E%7B1%2F7%7D ugly as well but i think we are supposed to use 'by parts'

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.0where did you get this question?

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1steward calculus advanved problem

shubhamsrg
 one year ago
Best ResponseYou've already chosen the best response.0what if we use the property integral ( f(x) from x=a to b = f(a+bx) from x= a to b )?

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1in this case a+b=0+1 int f(1x)=f(x)

shubhamsrg
 one year ago
Best ResponseYou've already chosen the best response.0yep, am not too sure if that'll work though, but probably should work ?

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1ok i have to go i;ll try it thanks to everyone for the effort

SithsAndGiggles
 one year ago
Best ResponseYou've already chosen the best response.0According to WA, the definite integral is 0: http://www.wolframalpha.com/input/?i=integrate+%28%281x%5E7%29%5E%281%2F3%29++%281x%5E3%29%5E%281%2F7%29%29+over+%5B0%2C1%5D Maybe there's some detail we're not getting about the function itself.

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1interesting result maybe this property is because of the function is actually an inverse of itself i mean \[f(x)=\sqrt[3]{1x^7}\] then \[f^{1}(x)=\sqrt[7]{1x^3}\] should this mean anything

Jonask
 one year ago
Best ResponseYou've already chosen the best response.1\[\int_0^1 f(x)f^{1}(x) \space dx\] \[f(1)=f^{1}(1)=0\]

experimentX
 one year ago
Best ResponseYou've already chosen the best response.2this is a famous question on M.SE
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