Question

求不定积分 1.∫1/(1+√x)dx 2.∫1/(1+√x) dx 3.∫arctanx/(1+x²) dx

Answer 1

1 令x=t^2

原式＝∫2t/(1+t)dt=2t-∫2/(1+t)dt=2t-2ln(1+t) +c

2,同1一样的题目.

3,原式＝∫arctanxdarctanx=1/2arctan^2 x+c

4,原式=∫cost dt^2 =∫2tcostdt=∫2tdsint= 2tsint-2∫sintdt=2tsint+2cost+c

=2√x sin√x +2cos√x +c