∫1/cos^3(x)dx = ∫cos(x)/cos^4(x) dx= ∫cos(x)/{1-sin^2(x)}^2 dx、sin(x)=t とおいて
∫1/(1-t^2)^2 dt = ∫1/{(1+t)(1-t)}^2 dt = (1/4)∫1/(1+t)^2 + 1/(1-t)^2 + 1/(1+t) + 1/(1-t) dt