怎样求表达式(x^2+y^2+z^2)^(3/2)只对x积分?

怎样求表达式(x^2+y^2+z^2)^(3/2)只对x积分?
怎样求表达式(x^2+y^2+z^2)^(3/2)只对x积分?

怎样求表达式(x^2+y^2+z^2)^(3/2)只对x积分?
结果是 x / (x^2+y^2+z^2)^(1/2)
先计算 I = ∫ 1 / (x²+a²)^(3/2) dx
设 x = a tant,
I = 1/a² ∫ cost dt = 1/a² sint + C
= 1/a² tant / sect + C
= (1/a²) x / √(x²+a²) + C