xdx/(x2+r2)^3/2的积分

题目详情

xdx/(x2+r2)^3/2的积分

▼优质解答

答案和解析

∫ x/(x² + r²)^(3/2) dx
= (1/2)∫ d(x²) / √(x² + r²)^(3/2)
= (1/2)∫ d(x² + r²) / √(x² + r²)^(3/2)
= (1/2) * (x² + r²)^(-1/2) / (-1/2) + c
= -1/√(x² + r²) + c

看了 xdx/(x2+r2)^3/...的网友还看了以下：