积分上限2,积分下限1,求√x*lnx的定积分,

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积分上限2,积分下限1,求√x*lnx的定积分,

积分上限2,积分下限1,求√x*lnx的定积分,
积分上限2,积分下限1,求√x*lnx的定积分,

积分上限2,积分下限1,求√x*lnx的定积分,
解法如下:
∫(1→2)√x*lnxdx
=(2/3)∫(1→2)lnxd x^(3/2) ←使用分部积分法
=(2/3)x^(3/2)lnx(1→2)-(2/3)∫(1→2)x^(3/2)d lnx
=(4√2*ln2)/3-(2/3)∫(1→2)x^(1/2)dx
=(4√2*ln2)/3-(4/9)(2√2-1)
以上答案仅供参考,

∫(1->2) lnx√x dx
= (2/3)∫(1->2) lnx d x^(3/2)
= (2/3)[x^(3/2) .lnx](1->2)- (2/3) ∫(1->2) x^(1/2) dx
=(2/3)( 2^(3/2) ln2) - (4/9)[ x^(3/2)](1->2)
=(2/3)( 2^(3/2) ln2) - (4/9)( 2^(3/2) -1 )