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(1 - x^3)^n integration. limits 0 to 1 ??

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try trig sub x^3 = sin^2u
hmm.. i'll try it once and get back to you..
if that doesn't work, do u= 1-x^3

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Other answers:

how ould that help? @hartnn
du = -3x^2 dx du = - 3(1-u)^(2/3)dx du/[- 3(1-u)^(2/3)] = dx just trying.......
intigrate with respect to x or n?
-x^3/ln(1-x^3) With respect to n
@experimentX yes i did the same. i think i got it now.. thank you..
this should end up around beta function
is this from Gamma Function ?
\[2/9\,{\frac {\Gamma \left( n+1 \right) \pi \,\sqrt {3}}{\Gamma \left( 2/3 \right) \Gamma \left( n+4/3 \right) }} \] gamma
because it gets the form u^n (1-u)^n
u^n (1-u)^m
oh and i used maple got no idea how to do it :P
\[ \frac{1}{3} \beta(2(n+1), 4/3)) = \]
Umm, can binomial theorem help with this?
\[ \Large (a+b)^n = \sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^{k} \]We let \(a = 1\) and \(b = -x^3\)?
can anybody integrate 2/3 [(1-t^2) / (t)^1/3] dt.. from 0 to 1.. i reached till here..
Like what about:\[ \Large \int_0^1\sum_{k=0}^{n}\binom{n}{k}(-x^3)^{k}dx \]
how u got that ?
@wio no idea about it.. its a grade 12 level question.. lol..
@experimentX 's method..
that's a good strategy!!
infinity to 2/3 [(1-t^2) / (t)^1/3]
i don't think this can be solved without beta functions, did u go to wiki link of beta function ? i am talking about this..
@hartnn hmm.. i gotta read beta function once..
thats easy to integrate just seperate the denominator.
t^(-1/3) - t^(-5/3)
i missed the n.. i think i gota read the beta/gamma function once.. thank you everyone..
yup, whether u put, u=1-x^3 or x^3 = sin^2 u you'll end up with one of the form of beta function.
for the last one \[ \frac 1 3 \times 2 \int_0^{\pi \over 2} \cos^{2(n+1) - 1}(x) \sin ^{\frac 4 3 - 1 }(x) dx = \frac 13 \beta (n+1, \frac 23 ) = \frac 13 \frac{\Gamma(n+1) \Gamma(2/3)}{\Gamma(n+4/3) } \]
something went wrong

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