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experimentXBest ResponseYou've already chosen the best response.0
try trig sub x^3 = sin^2u
 one year ago

yrelhan4Best ResponseYou've already chosen the best response.0
hmm.. i'll try it once and get back to you..
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
if that doesn't work, do u= 1x^3
 one year ago

yrelhan4Best ResponseYou've already chosen the best response.0
how ould that help? @hartnn
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
du = 3x^2 dx du =  3(1u)^(2/3)dx du/[ 3(1u)^(2/3)] = dx just trying.......
 one year ago

timo86mBest ResponseYou've already chosen the best response.0
intigrate with respect to x or n?
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
dw:1356588801737:dw
 one year ago

timo86mBest ResponseYou've already chosen the best response.0
x^3/ln(1x^3) With respect to n
 one year ago

yrelhan4Best ResponseYou've already chosen the best response.0
@experimentX yes i did the same. i think i got it now.. thank you..
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
this should end up around beta function http://en.wikipedia.org/wiki/Beta_function#Properties
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
is this from Gamma Function ?
 one year ago

timo86mBest ResponseYou've already chosen the best response.0
\[2/9\,{\frac {\Gamma \left( n+1 \right) \pi \,\sqrt {3}}{\Gamma \left( 2/3 \right) \Gamma \left( n+4/3 \right) }} \] gamma
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
because it gets the form u^n (1u)^n
 one year ago

timo86mBest ResponseYou've already chosen the best response.0
oh and i used maple got no idea how to do it :P
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
http://www.wolframalpha.com/input/?i=integrate+%281x%5E3%29%5En+dx+from+0+to+1
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
\[ \frac{1}{3} \beta(2(n+1), 4/3)) = \]
 one year ago

wioBest ResponseYou've already chosen the best response.0
Umm, can binomial theorem help with this?
 one year ago

wioBest ResponseYou've already chosen the best response.0
\[ \Large (a+b)^n = \sum_{k=0}^{n}\binom{n}{k}a^{nk}b^{k} \]We let \(a = 1\) and \(b = x^3\)?
 one year ago

yrelhan4Best ResponseYou've already chosen the best response.0
can anybody integrate 2/3 [(1t^2) / (t)^1/3] dt.. from 0 to 1.. i reached till here..
 one year ago

wioBest ResponseYou've already chosen the best response.0
Like what about:\[ \Large \int_0^1\sum_{k=0}^{n}\binom{n}{k}(x^3)^{k}dx \]
 one year ago

yrelhan4Best ResponseYou've already chosen the best response.0
@wio no idea about it.. its a grade 12 level question.. lol..
 one year ago

yrelhan4Best ResponseYou've already chosen the best response.0
@experimentX 's method..
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
that's a good strategy!!
 one year ago

timo86mBest ResponseYou've already chosen the best response.0
infinity to 2/3 [(1t^2) / (t)^1/3]
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
i don't think this can be solved without beta functions, did u go to wiki link of beta function ?
 one year ago

yrelhan4Best ResponseYou've already chosen the best response.0
http://www.wolframalpha.com/input/?i=integrate+%5B%281t%5E2%29+%2F+%28t%29%5E1%2F3%5D+dt+from+0+to+1 i am talking about this..
 one year ago

yrelhan4Best ResponseYou've already chosen the best response.0
@hartnn hmm.. i gotta read beta function once..
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
http://www.wolframalpha.com/input/?i=integrate+%5B%281t%5E2%29+%2F+%28t%29%5E1%2F3%5D+dt
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
thats easy to integrate just seperate the denominator.
 one year ago

yrelhan4Best ResponseYou've already chosen the best response.0
i missed the n.. i think i gota read the beta/gamma function once.. thank you everyone..
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
yup, whether u put, u=1x^3 or x^3 = sin^2 u you'll end up with one of the form of beta function.
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
for the last one \[ \frac 1 3 \times 2 \int_0^{\pi \over 2} \cos^{2(n+1)  1}(x) \sin ^{\frac 4 3  1 }(x) dx = \frac 13 \beta (n+1, \frac 23 ) = \frac 13 \frac{\Gamma(n+1) \Gamma(2/3)}{\Gamma(n+4/3) } \]
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
something went wrong
 one year ago
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