求不定积分(x^2/√2-x^2)dx.

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求不定积分(x^2/√2-x^2)dx.求不定积分(x^2/√2-x^2)dx.求不定积分(x^2/√2-x^2)dx.设x=√2sint,则dx=√2costdt∫x^2/√(2-x^2)dx=∫2

求不定积分(x^2/√2-x^2)dx.
求不定积分(x^2/√2-x^2)dx.

求不定积分(x^2/√2-x^2)dx.
设 x = √2 sint,则 dx = √2cost dt
∫x^2/√(2-x^2) dx
=∫2(sint)^2/[√2 cost] * (√2cost) dt
=∫2(sint)^2 dt
=∫(1-cos2t)dt
=t - ∫cos2t dt
=t -1/2 sin2t + C
=arcsin(x/√2) - x*√(2-x^2) + C

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