Question

1/根号x*(1+x)求不定积分;1/1+cosx求不定积分;sinx/1+cosx求不定积分

Answer 1

1、令x=tan^2t dx=2tantsec^2tdt

原式=∫2tantsec^2tdt/tantsec^2t

=2∫dt

=2t+C

=2arctan(√x)+C

2、∫dx/(1+cosx)

=∫dx/2cos^2(x/2)

=∫sec^2(x/2)d(x/2)

=tan(x/2)+C

3、∫sinxdx/(1+cosx)

=∫2sin(x/2)cos(x/2)dx/2cos^2(x/2)

=2*∫tan(x/2)d(x/2)

=-2ln|cos(x/2)|+C