Write a value of ∫ tan3xsec2xdx.

1.	Write a value of ∫ tan3xsec2xdx.
Answer» Given, ∫ tan³xsec²xdx let tan x = t Differentiating on both sides we get, sec²x dx = dt Substituting above equation in ∫tan³x sec²x dx we get, = ∫t³ dt = \(\frac{t^4}{4}\)+ c = \(\frac{tan^4x}{4}\) + c

Answer»

Given,

∫ tan³xsec²xdx

let tan x = t

Differentiating on both sides we get,

sec²x dx = dt

Substituting above equation in ∫tan³x sec²x dx we get,

= ∫t³ dt

= \(\frac{t^4}{4}\)+ c

= \(\frac{tan^4x}{4}\) + c

Discussion