Question

不定积分∫根号x^2-1/xdx ,根号是到1的,要看清楚, ∫1/根号x(x+1)dx . 根号只到前面的x详细解答…

Answer 1

1、

令x=secy,dx=secytany dy

∫√(x²-1)/x dx

=∫tany/secy*secytany dy

=∫tan²y dy

=∫(sec²y-1) dy

=tany-y + C

=√(x²-1)-arcsecx + C

2、

∫1/[√x(x+1)] dx

=2∫1/[2√x*(x+1)] dx

=2∫1/[1+(√x)²] d√x

=2arctan(√x) + C