求不定积分,见图

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求不定积分,见图

x=sint,√(1-x^2) = cost,dx = cost dt
原式= ∫ cost/(sint+cost) dt
= (1/2) ∫ [ 1 + (cost-sint)/(sint+cost)] dt
= (1/2) [ 1 + ln(sint + cost) ] + C
= (1/2)arcsinx + (1/2) ln( x+ √(1-x^2) ) + C

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