方法一:把dx/(1+tanx)化成cosxdx/(cosx+sinx)=d(sinx)/根号2*sin(x+派/4)
=(1/根号2)d(sin(x+派/4))/sin(x+派/4)=(1/根号2)*
ln(sin(x+派/4))+c
方法二:2∫dx/(1+tanx)
=∫2cosxdx/(sinx+cosx)
=∫[(cosx+sinx)+(cosx-sinx)]dx/(cosx+sinx)
=∫1*dx+∫(cosx-sinx)dx/(sinx+cosx)]
=x+∫d(sinx+cosx)/(sinx+cosx)
=x+ln(sinx+cosx)+C'
所以∫dx/(1+tanx)=x/2+(1/2)ln(sinx+cosx)+C.
我知道二肯定对,但一为什么不对呢?求高人解答