above equation can be solve by using one formula that is (i+ tan 2 x=sec 2 x) I = ∫ sec 4 x dx = ∫ sec 2 x sec 2 x dx = ∫ sec 2 x ( 1 + tan 2 x ) dx = ∫ sec 2 x dx + ∫ sec 2 x tan 2 x dx Put tanx=t in above equation so that sec 2 xdx=dt

Evaluate

above equation can be solve by using one formula that is (i+ tan²x=sec²x)

_{I = ∫ sec}⁴x dx

_{= ∫ sec}²x sec²x dx

_{= ∫ sec}²x ( 1 + tan²x ) dx

_{= ∫ sec}²x dx + ∫ sec²x tan²x dx

Put tanx=t in above equation so that sec²xdx=dt