Question

用换元法求1加根号x分之dx的不定积分

Answer 1

∫dx/(1+√x

设√x=t,则有：

∫dt^2/(1+t)

=2∫tdt/(t+1)

=2∫(t+1-1)dt/(t+1)

=2∫dt-2∫dt/(t+1)

=2t-2ln(t+1)+c

=2√x-2ln(√x+1)+c.