1/根号下x(4-x)的原函数?

题目详情

1/根号下x(4-x)的原函数?

▼优质解答

答案和解析

∫1/根号[x(4-x)]dx
=∫1/根号[4x-x^2]dx
=∫1/根号[4-4+4x-x^2]dx
=∫1/根号[4-(x-2)^2]dx
=∫1/根号[1-(x/2-1)^2]d(x/2)
=arcsin(x/2-1)+C

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