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换元x＝sint，则dx＝costdt，原式＝∫costdt/(sint+cost)
cost/(sint+cost)＝1/2×(cost+sint+cost-sint)/(sint+cost)＝1/2×[1＋(cost-sint)/(sint+cost)]
所以，原式＝∫costdt/(sint+cost)＝1/2×∫[1＋(cost-sint)/(sint+cost)]dt＝1/2×[t＋∫1/(sint+cost)d(sint+cost)]＝1/2×[t＋ln|sint+cost|]＋C＝1/2×[arcsinx＋ln|(x＋√(1-x^2)|]＋C
cost/(sint+cost)＝1/2×(cost+sint+cost-sint)/(sint+cost)＝1/2×[1＋(cost-sint)/(sint+cost)]
所以，原式＝∫costdt/(sint+cost)＝1/2×∫[1＋(cost-sint)/(sint+cost)]dt＝1/2×[t＋∫1/(sint+cost)d(sint+cost)]＝1/2×[t＋ln|sint+cost|]＋C＝1/2×[arcsinx＋ln|(x＋√(1-x^2)|]＋C
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