求不定积分:∫dX/sinX+cosX
问题描述:
求不定积分:∫dX/sinX+cosX
答
∫dx/(sinx+cosx)
=√2∫ dx/(sin(x+π/4)
= √2∫ csc(x+π/4)) dx
=√2ln |csc(x+π/4) - cot(x+π/4)| + C