The integral ∫ π 6 π 3 tan 3 x · sin 2 3 x 2 sec 2 x · sin 2 3 x + 3 tan x · sin 6 x d x is equal to:

Step-by-step solution

Rearranging, we get, ∫ π / 6 π / 3 d d x tan 4 x 2 · sin 4 3 x + tan 4 x · d d x sin 4 3 x 2 d x = 1 2 ∫ π / 6 π / 3 d d x tan 4 x · sin 4 3 x d x = 1 2 tan 4 x · sin 4 3 x π / 6 π / 3 = 1 2 3 4 × 0 - 1 3 4 × 1 = - 1 2 × 1 9 = - 1 18