Question

不定积分∫arctan根号x/根号x*1/(1+x)dx

Answer 1

∫(arctan√x)/[√x(1+x)] dx

=∫(arctan√x)/(1+x) d(2√x)

=2∫(arctan√x)/[1+(√x)²] d(√x)

=2∫arctan√x d(arctan√x),where ∫dx/(1+x²)=arctanx+C

=2*(1/2)(arctan√x)²+C

=(arctan√x)²+C