The value of the definite integral ∫ π / 24 5 π / 24 d x 1 + tan 2 x 3 is

Step-by-step solution

Let I = ∫ π / 24 5 π / 24 d x 1 + tan 2 x 3 ⇒ I = ∫ π / 24 5 π / 24 ( cos 2 x ) 1 / 3 ( cos 2 x ) 1 / 3 + ( sin 2 x ) 1 / 3 d x       . . . i ⇒ I = ∫ π / 24 5 π / 24 cos 2 π 4 - x 1 3 cos 2 π 4 - x 1 3 + sin 2 π 4 - x 1 3 d x ∫ a b f x d x = ∫ a b f a + b - x d x So, I = ∫ π / 24 5 π / 24 ( sin 2 x ) 1 / 3 ( sin 2 x ) 1 / 3 + ( cos 2 x ) 1 / 3 d x       . . . ii Adding the equation (i