求不定积分,如图所示.

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求不定积分,如图所示.
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求不定积分,如图所示.
求不定积分,如图所示.

求不定积分,如图所示.
令x=根号(1-t)
dx=(-1/2)(1-t)^(-1/2)dt
(1-t)^(-1/2)dt=-2dx
x^2=1-t
t=1-x^2
原积分=积分(-2dx)/(1-x^2)
注意2/(x^2-1)=1/(x-1)-1/(x+1)
=积分dx/(x-1)-积分dx/(x+1)
=ln|x-1|-ln|x+1|+C
=ln|(x-1)/(x+1)|+C
=ln|(根号(1-t)-1)/(根号(1-t)+1)|+C