被积函数定义域为{x|-1≤x≤1且x≠-√2/2}
设x=sint(-π/2≤t≤π/2且t≠-π/4),则dx=costdt,√(1-x²)=cost,t=arcsinx
原式=∫costdt/(sint+cost)
=1/2*∫[(cost+sint)+(cost-sint)]dt/(cost+sint)
=1/2*∫dt+1/2*∫d(sint+cost)/(sint+cost)
=t/2+1/2*ln|sint+cost|+C
=1/2*(arcsinx+ln|x+√(1-x²)|)+C
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