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

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

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

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

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

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

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

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

JonaskBest ResponseYou've already chosen the best response.1
http://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'
 one year ago

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

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

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

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

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

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

SithsAndGigglesBest ResponseYou've already chosen the best response.0
According 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.
 one year ago

JonaskBest ResponseYou've already chosen the best response.1
interesting 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
 one year ago

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

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