∫1/[1+(1-x^2)^(1/2)]dx,求解答过程

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∫1/[1+(1-x^2)^(1/2)]dx,求解答过程∫1/[1+(1-x^2)^(1/2)]dx,求解答过程∫1/[1+(1-x^2)^(1/2)]dx,求解答过程∫1/[1+(1-x^2)^(1

∫1/[1+(1-x^2)^(1/2)]dx,求解答过程
∫1/[1+(1-x^2)^(1/2)]dx,求解答过程

∫1/[1+(1-x^2)^(1/2)]dx,求解答过程
∫1/[1+(1-x^2)^(1/2)]dx
= ∫1/[1+cost]d(sint) (令x=sint)
=∫(cost)/(1+cost)dt
=∫dt-∫dt/(1+cost)
=t+ctgt-csct+C
=arcsinx+ctgarcsinx-1/x +C
=arcsinx + (1-x^2)^(1/2)/x +C

1除以1+(1-x^2)^2/2乘以dx=2/2+(1-x^2.)^2乘以dx=2dx/2+(1-x^2)^2