高数 ∫x^(2/3)log(2)(x)dx
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高数 ∫x^(2/3)log(2)(x)dx
高数
∫x^(2/3)log(2)(x)dx
高数 ∫x^(2/3)log(2)(x)dx
分部积分法,见图
分部积分:
∫x^(2/3)log(2)(x)dx
=(3/5)∫log(2)(x)d[x^(5/3)]
=(3/5){x^(5/3)log(2)(x)-∫x^(5/3)dlog(2)(x)}
=(3/5){x^(5/3)log(2)(x)-∫x^(5/3)(1/xln2)dx}
=(3/5){x^(5/3)log(2)(x)-∫x^(2/3)/ln2}
=(3/5){x^(5/3)log(2)(x)-(3/5ln2)x^(5/3)}
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