一道微积分题，求解答需要过程？

Question

如题所述

Answer 1

∫x^3.√(4-x^2) dx
=-(1/3)∫x^2. d(4-x^2)^(3/2)
=-(1/3)x^2. (4-x^2)^(3/2) +(2/3)∫x (4-x^2)^(3/2) dx
=-(1/3)x^2. (4-x^2)^(3/2) -(2/15)∫ d(4-x^2)^(5/2)
=-(1/3)x^2. (4-x^2)^(3/2) -(2/15)(4-x^2)^(5/2) +C

Answer 2

换元积分，令x＝2sint，代入即可。或者把dx凑成dx²，也可求出原函数。