The value of the integral int π/24 5 π/24 frac dx 1+sqrt[3] tan 2 x is :

Mathematics · Definite Integration

JEE Main 2026 — 23 January, Morning Shift — Question 10

The value of the integral $\int_{\frac{\pi}{24}}^{\frac{5 \pi}{24}} \frac{\mathrm{dx}}{1+\sqrt[3]{\tan 2 \mathrm{x}}}$ is :

$I=\int_{\frac{\pi}{24}}^{\frac{5 \pi}{24}} \frac{d x}{1+\sqrt[3]{\tan 2 x}}$

Apply king $I=\int_{\frac{\pi}{24}}^{\frac{5 \pi}{24}} \frac{d x}{\sqrt[3]{\tan 2\left(\frac{\pi}{4}-x\right)}}$

\begin{gathered} =\int_{\frac{\pi}{24}}^{\frac{5 \pi}{24}} \frac{d x}{1+\sqrt[3]{\cot 2 x}} \end{gathered}

Add $(1)+(2)\Rightarrow 2 I=\int_{\frac{\pi}{24}}^{\frac{5 \pi}{24}}d x$

$\mathrm{I}=\frac{1}{2}\left(\frac{\pi}{6}\right)=\frac{\pi}{12}$

Answer key and solution verified before publishing.

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