>>745
∫{1/(t^2+1)^3}dt=∫(t^2+1-t^2)/(t^2+1)^3 dt=∫1/(t^2+1)^2 dt-∫t*{t/(t^2+1)^3} dt

=∫1/(t^2+1)^2 dt-{(-t/4)*(1/(t^2+1)^2)+(1/4)*∫1/(t^2+1)^2 dt}

=(3/4)*∫1/(t^2+1)^2 dt+(t/4)*1/(t^2+1)^2
ここで∫1/(t^2+1)^2 dt=∫1/(t^2+1) dt-∫t*(t/(t^2+1)^2 dt=∫1/(t^2+1) dt
-{(-t/2)*1/(t^2+1)+(1/2)*∫1/(t^2+1) dt}=(1/2)*(arctan(t)+t/(t^2+1))

よって(与式)=(1/8)*(3*arctan(t)+t*(3*t^2+5)/(t^2+1)^2)