不定积分,
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不定积分,
不定积分,
不定积分,
令x=sint
∴dx=cost dt
√(1-x^2)=cost
∴原式=∫sin^2 t *cost dt /(1+cost)
=∫(1-cos^2 t) *costdt /(1+cost)
=∫(1-cost)costdt
=∫costdt -∫cos^2 t dt
=sint -1/2∫ 2cos^2 t dt
=sint -1/2∫ (cos2t +1) dt
=sint -1/2∫cos2t dt -1/2∫dt
=sint -sin2t /2 -t/2 +C
=x -x√(1-x^2) -arcsinx /2 +C