Evaluate: ∫ tan3 x .sec6x dx
= ∫ tan3 x (1 + tan2 x)2 sec2 x dx
= ∫ t3 (1 + t2)2 dt,
Let tan x = t
= sec2 x dx = dt
= ∫ t3 (t4 + 2t2 + 1) dt
= ∫ (t7+ 2t5 + t3) dt
= ((t8/ 8) + (t3/ 3) + (t4/ 4)) + c
= ((tan8 x/ 8) + (tan3 x/ 3) + (tan4 x/ 4)) + c