求解这道高数的不定积分 谢谢
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∫x^3(lnx)^2dx
=(1/4)∫(lnx)^2d(x^4)
=(1/4)(x^4)(lnx)^2-(1/4)∫(x^4)d((lnx)^2)
=(1/4)(x^4)(lnx)^2-(1/4)∫(x^4)2lnx*(1/x)dx
=(1/4)(x^4)(lnx)^2-(1/2)∫(x^3)lnxdx
=(1/4)(x^4)(lnx)^2-(1/8)∫lnxd(x^4)
=(1/4)(x^4)(lnx)^2-(1/8)(x^4)lnx+(1/8)∫(x^4)d(lnx)
=(1/4)(x^4)(lnx)^2-(1/8)(x^4)lnx+(1/8)∫(x^4)(1/x)dx
=(1/4)(x^4)(lnx)^2-(1/8)(x^4)lnx+(1/8)∫(x^3)dx
=(1/4)(x^4)(lnx)^2-(1/8)(x^4)lnx+(1/32)(x^4)+C
=(1/4)∫(lnx)^2d(x^4)
=(1/4)(x^4)(lnx)^2-(1/4)∫(x^4)d((lnx)^2)
=(1/4)(x^4)(lnx)^2-(1/4)∫(x^4)2lnx*(1/x)dx
=(1/4)(x^4)(lnx)^2-(1/2)∫(x^3)lnxdx
=(1/4)(x^4)(lnx)^2-(1/8)∫lnxd(x^4)
=(1/4)(x^4)(lnx)^2-(1/8)(x^4)lnx+(1/8)∫(x^4)d(lnx)
=(1/4)(x^4)(lnx)^2-(1/8)(x^4)lnx+(1/8)∫(x^4)(1/x)dx
=(1/4)(x^4)(lnx)^2-(1/8)(x^4)lnx+(1/8)∫(x^3)dx
=(1/4)(x^4)(lnx)^2-(1/8)(x^4)lnx+(1/32)(x^4)+C
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