∫(-π/2,0) cost/√(1+cost)dt
=∫(-π/2,0)(2cos²2t-1)/(√2cos2t)dt
=∫(-π/2,0)(2cos²2t-1)/(√2cos2t)dt
=∫(-π/2,0)(2cos²2t-1)/(√2cos2t)dt
2t=x
t=-π/2x=-π
=1/2∫(-π,0)(2cos²x-1)/(√2cosx)dx
=√2/2∫(-π,0)cosxdx-1/2∫(-π,0)1/(√2cosx)dx
(-π,0)区间cosx的积分为0
=0