求∫x*(1+x)∧1/2dx

题目详情

求∫x*(1+x)∧1/2dx

▼优质解答

答案和解析

∫ x√(1 + x) dx
= ∫ [(1 + x) - 1]√(1 + x) dx
= ∫ [(1 + x)^(3/2) - √(1 + x)] dx
= (2/5)(1 + x)^(5/2) - (2/3)(1 + x)^(3/2) + C
= (2/15)(3x - 2)(x + 1)^(3/2) + C

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