∫ tan²x dx
= ∫ (sec²x - 1) dx,恒等式1 + tan²x = sec²x
= ∫ sec²x dx - ∫ dx
= tanx - x + C令x = 3secz，dx = 3secztanz dz，x > 3 > 0∫ √(x² - 9)/x dx= ∫ √(9sec²z - 9)/(3secz) * (3secztanz dz)= ∫ |3tanz| * tanz dz= 3∫ tan²z dz= 3(tanz - z) + C= 3√(sec²z - 1) - 3z + C= 3√[(x/3)² - 1] - 3arcsec(x/3) + C= √(x² - 9) - 3arccos(3/x) + C