Question

谁能告诉我∫(2*arctan(x))/(1+x^2),x)怎麼算啊

Answer 1

∫(2arctanx)/(1+x²)dx

=∫2arctanxd(arctanx)

=(arctanx)²+C

或者令t=arctanx,则dt=dx/(1+x²)

∫(2arctanx)/(1+x²)dx

=∫2t·dt

=t²+C

=(arctanx)²+C