The value of the definite integral ∫ dx/1 + 3√tan 2x x ∈ [π/24, 5π/24] (1) π/3 (2) π/6 (3) π/12 (4) π/18

Question

The value of the definite integral

\(\int\limits_{\frac{\pi}{24}}^{\frac{5\pi}{24}}\)\(\frac{dx}{1+\sqrt[3]{tan2x}}\) is :

(1) \(\frac{\pi}{3}\)

(2) \(\frac{\pi}{6}\)

(3) \(\frac{\pi}{12}\)

(4) \(\frac{\pi}{18}\)

Answer 1

\(\Rightarrow\) 2I = \(\frac{4 \pi}{24}\) \(\Rightarrow\) I = \(\frac{\pi}{2}\)