∫dx/[(1+x)√1-2]

∫dx/[(1+x)√1-²]
【正确答案】：令x=sint，则dx=costdt于是∫dx/(1+x)√1-x²=∫costdt/(1+sint)cos=∫dt/(1+sint)=∫(1-sint)dt/cos²t=∫sec²tdt+∫(1/cos²t)dcost=tant-(1/cost)+C=x/√1-x²-1/√1-x²+C=-√[(1-x)/(1+x)]+C