in this integral we will use the formula 1+tan 2 x=sec 2 x, Then equation will be transform in below form- I = ∫tan 3 x sec 2 x sec 2 x dx = ∫tan 3 x (1 + tan 2 x) sec 2 x dx Now put tanx=t which means sec 2 xdx=dt, Now put the value of t,which is t=tanx in above integral-

Evaluate

in this integral we will use the formula 1+tan²x=sec²x,

_{Then equation will be transform in below form-}

_{I = ∫tan}³x sec²x sec²x dx

_{= ∫tan}³x (1 + tan²x) sec²x dx

Now put tanx=t which means sec²xdx=dt,

Now put the value of t,which is t=tanx in above integral-