第1个回答 2018-01-19
设x=sint
原式=∫ [1/(1+cost)]d(sint)
=∫[cost/(1+cost)]dt
=∫[(cost+1-1)/(1+cost)]dt
=∫dt-∫1/(1+cost)dt
=t-∫d(½t)/[cos²(½t) 倍角公式
=t-tan(½t)+C
=t-sint/(1+cost)+C 半角公式
=arcsinx-x/[1+√(1-x²)]+C
相似回答
设x=sint
原式=∫ [1/(1+cost)]d(sint)
=∫[cost/(1+cost)]dt
=∫[(cost+1-1)/(1+cost)]dt
=∫dt-∫1/(1+cost)dt
=t-∫d(½t)/[cos²(½t) 倍角公式
=t-tan(½t)+C
=t-sint/(1+cost)+C 半角公式
=arcsinx-x/[1+√(1-x²)]+C
