不定积分x^n*lnxdx
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∫x^n *lnx dx
= 1/(n+1)* ∫lnx dx^(n+1) (分部积分)
= 1/(n+1)* [x^(n+1)*lnx - ∫x^(n+1)dlnx]
= 1/(n+1)* [x^(n+1)*lnx - ∫x^n dx]
= 1/(n+1)* [x^(n+1)*lnx - 1/(n+1) * x^(n+1)] +C
= 1/(n+1)* x^(n+1)* [lnx - 1/(n+1)] +C C任意常数
= 1/(n+1)* ∫lnx dx^(n+1) (分部积分)
= 1/(n+1)* [x^(n+1)*lnx - ∫x^(n+1)dlnx]
= 1/(n+1)* [x^(n+1)*lnx - ∫x^n dx]
= 1/(n+1)* [x^(n+1)*lnx - 1/(n+1) * x^(n+1)] +C
= 1/(n+1)* x^(n+1)* [lnx - 1/(n+1)] +C C任意常数
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