Question

∫3x×dx/9+x²

Answer 1

问：∫3x×dx/9+x²

答：亲，为您找到一下两种解法

答：让 u = 9 + x²，那么 du/dx = 2x，dx = du/2x。将其代入积分式中得：∫(3x/(9+x²))dx = (3/2)∫(1/u)du = (3/2)ln|u| + C = (3/2)ln|9+x²| + C 因此，∫(3x/(9+x²))dx = (3/2)ln|9+x²| + C。

答：Let u = 9 + x², then du/dx = 2x and dx = du/2x. Substituting, the integral becomes: ∫(3x/(9+x²))dx = (3/2)∫(1/u)du = (3/2)ln|u| + C = (3/2)ln|9+x²| + C Therefore, ∫(3x/(9+x²))dx = (3/2)ln|9+x²| + C.