求不定积分x^2*arcsinxdx

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求不定积分x^2*arcsinxdx求不定积分x^2*arcsinxdx求不定积分x^2*arcsinxdx∫x^2*arcsinxdx=(1/3)∫arcsinxd(x^3)=(1/3)x^3arc

求不定积分x^2*arcsinxdx
求不定积分x^2*arcsinxdx

求不定积分x^2*arcsinxdx
∫x^2*arcsinx dx
=(1/3) ∫ arcsinx d(x^3)
= (1/3)x^3 arcsinx -(1/3) ∫ [x^3/√(1-x^2)] dx
=(1/3)x^3 arcsinx +(1/3) ∫ x^2 d√(1-x^2)
=(1/3)x^3 arcsinx +(1/3) x^2 .√(1-x^2) -(2/3)∫x√(1-x^2) dx
=(1/3)x^3 arcsinx +(1/3) x^2 .√(1-x^2) +(2/9)∫ d (1-x^2)^(3/2)
= (1/3)x^3 arcsinx +(1/3) x^2 .√(1-x^2) +(2/9)(1-x^2)^(3/2) + C