Question

Let In ∫tan x dx,(n> 1) . I⁴ + I⁶ = a tan⁵x + bx⁵ + C, where C is a constant of integration, then the ordered pair (a, b) is equal to

$open parentheses negative 1 fifth comma 0 close parentheses$
$open parentheses negative 1 fifth comma 1 close parentheses$
$open parentheses 1 fifth comma 0 close parentheses$
$open parentheses 1 fifth comma negative 1 close parentheses$

Solution

open parentheses 1 fifth comma 0 close parentheses

I4 +I6 = ∫(tan⁴x + tan⁶x) dx
= ∫tan⁴ x sec² x dx
= 1/5 tan⁵ x + c
⇒ a = 1/5, b = 0

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