设x=3sint∫x^2/根号下(9-X^2) dx=∫9(sint)^2*3costdt/3cost=(9/2)∫(1-cos2t)dt=(9/4)∫(1-cos2t)d(2t)=(9/4)(2t-sin2t)+C=(9/2)(t-sintcost)+C=(9/2)[arcsin(x/3)-x/3*根号(9-x^2)]+C
求数学大神 问 不定积分 根号下(ax-x^2) dx 怎么做？
设x=3sint∫x^2/根号下(9-X^2) dx=∫9(sint)^2*3costdt/3cost=(9/2)∫(1-cos2t)dt=(9/4)∫(1-cos2t)d(2t)=(9/4)(2t-sin2t)+C=(9/2)(t-sintcost)+C=(9/2)[arcsin(x/3)-x/3*根号(9-x^2)]+C