求不定积分x^2*arcsinxdx

vfory2022-10-04 11:39:541条回答

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毛毛虫来了共回答了19个问题 | 采纳率84.2%: ∫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; 1年前