求不定积分∫x^2/根号下(9-X^2) dx

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求不定积分∫x^2/根号下(9-X^2)dx求不定积分∫x^2/根号下(9-X^2)dx求不定积分∫x^2/根号下(9-X^2)dx设x=3sint∫x^2/根号下(9-X^2)dx=∫9(sint)

求不定积分∫x^2/根号下(9-X^2) dx
求不定积分∫x^2/根号下(9-X^2) dx

求不定积分∫x^2/根号下(9-X^2) dx
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

分部积分一次后,利用三角代换即可求出积分