积分∫x^3*sqr(1-x^2)dx
问题描述：
积分∫x^3*sqr(1-x^2)dx
答
∫x^3*sqr(1-x^2)dx =-1/2∫x²√(1-x²)d(1-x²)=1/2∫[(1-x²)-1]√(1-x²)d(1-x²)=1/2∫[(1-x²)^(3/2)-(1-x²)^(1/2)]d(1-x²)=1/2[(2/5)(1-x²)^(5/2)-(2/3)(1-x&sup...