※ 引述《coolbaby119 (187無聊小豐)》之銘言：
: (2)
: ∫x^3˙sinx dx
一直by parts消掉x的次方就好
∫(x^3)sinxdx =∫(x^3)d(-cosx)= -(x^3)cosx+∫(3x^2)cosxdx
= -(x^3)cosx+∫(3x^2)d(sinx)
= -(x^3)cosx+(3x^2)sinx-∫(6x)sinxdx
= -(x^3)cosx+(3x^2)sinx+∫(6x)d(cosx)
= -(x^3)cosx+(3x^2)sinx+(6x)cosx-∫6cosxdx
= -(x^3-6x)cosx+(3x^2-6)sinx+C
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