∫dx/√(x^2-a^2)
令x=asect
dx=atantsectdt
=∫atantsect/√(a^2(sect)^2-a^2) dt
=∫atantsect/(atant)dt
=∫sectdt
=ln|sect+tant|+C
sect=x/a
tant=√[(sect)^2-1]=[√(x^2-a^2)]/a
∫dx/√(x^2-a^2)
=ln|sect+tant|+C
=ln|x/a+[√(x^2-a^2)]/a|+C
=ln|x+√(x^2-a^2)|-lna+C
=ln|x+√(x^2-a^2)|+C