Write a value of ∫ tan6x sec2x dx.

1.	Write a value of ∫ tan6x sec2x dx.
Answer» Given, ∫ tan⁶x sec²x dx let tan x = t Differentiating on both sides we get, sec²x dx = dt Substituting above equation in ∫ tan³x sec²x dx we get, =∫t⁶ dt = \(\frac{t^7}{7}\) + c = \(\frac{tan^7x}{7}\) + c

Answer»

Given,

∫ tan⁶x sec²x dx

let tan x = t

Differentiating on both sides we get,

sec²x dx = dt

Substituting above equation in ∫ tan³x sec²x dx we get,

=∫t⁶ dt

= \(\frac{t^7}{7}\) + c

= \(\frac{tan^7x}{7}\) + c

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