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求各位大神给出详细的解答过程
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解:
令arcsinx=t,则x=sint
∫(arcsinx)²dx
=∫t²d(sint)
=t²·sint-∫sintd(t²)
=t²·sint-2∫tsintdt
=t²·sint+2∫td(cost)
=t²·sint+2tcost-2∫costdt
=t²·sint+2tcost-2sint +C
=x·(arcsinx)²+2√(1-x²)·arcsinx-2x +C
令arcsinx=t,则x=sint
∫(arcsinx)²dx
=∫t²d(sint)
=t²·sint-∫sintd(t²)
=t²·sint-2∫tsintdt
=t²·sint+2∫td(cost)
=t²·sint+2tcost-2∫costdt
=t²·sint+2tcost-2sint +C
=x·(arcsinx)²+2√(1-x²)·arcsinx-2x +C
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