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Question-131288




Question Number 131288 by mohammad17 last updated on 03/Feb/21
Answered by liberty last updated on 11/Feb/21
L=∫ (√((1−3x^(−3) )/x^8 )) dx = ∫ x^(−4)  (√(1−3x^(−3) )) dx  change of variable : (√(1−3x^(−3) )) = h or 1−3x^(−3) =h^2   ⇒9x^(−4)  dx = 2h dh  L = (2/9)∫ h^2  dh = (2/(27))h^3  + c   L=(2/(27)) (√((((x^3 −3)/x^3 ))^3 )) + c =(2/(27))(((x^3 −3)/x^3 )) (√((x^3 −3)/x^3 )) + c
L=13x3x8dx=x413x3dxchangeofvariable:13x3=hor13x3=h29x4dx=2hdhL=29h2dh=227h3+cL=227(x33x3)3+c=227(x33x3)x33x3+c
Answered by Dwaipayan Shikari last updated on 03/Feb/21
∫(√((x^3 −3)/x^(11) )) dx  =∫(1/x^4 )(√(1−(3/x^3 ))) dx  =(1/9)∫(9/x^4 )(√(1−(3/x^3 ))) dx=(2/(27))(1−(3/x^3 ))^(3/2) +C
x33x11dx=1x413x3dx=199x413x3dx=227(13x3)32+C