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3x-x-3-1-3-dx-




Question Number 205294 by depressiveshrek last updated on 15/Mar/24
∫((3x−x^3 ))^(1/3) dx
3xx33dx
Answered by Frix last updated on 15/Mar/24
∫(3x−x^3 )^(1/3) dx =^(t=(x^2 /3))  (3/2)∫t^(−(1/3)) (1−t)^(1/3) dt=  =(3/2)t^(2/3)  _2 F_1  (−(1/3), (2/3); (5/3); t) =  =(((3x^4 ))^(1/3) /2) _2 F_1  (−(1/3), (2/3); (5/3); (x^2 /3)) +C
(3xx3)13dx=t=x2332t13(1t)13dt==32t232F1(13,23;53;t)==3x4322F1(13,23;53;x23)+C

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