Question

∫1/(x4（√x2-1)） dx

Answer 1

令x=secu,则dx=secu·tanu du∫1/[x^4·√(x^2-1)]dx=∫(cosu)^3 du=∫[1-(sinu)^2]cosu du=∫[cosu-(sinu)^2·cosu] du=∫cosu du-∫(sinu)^2·cosudu=sinu-∫(sinu)^2 d(sinu)=sinu-1/3·(sinu)^3+C=√(1-1/x^2)-1...