Mathematics · 2021
JEE Main · 31 August 2021, Shift 2 · Q86
If ∫ (sin x)/(sin^3 x+ cos^3 x) d x=α log_e |1+ tan x|+β log_e |1- tan x+ tan^2 x|+γ tan^-1((2 tan x-1)/(√ 3))+ C, when C is constant of integration,…
If $\displaystyle \int \frac{\sin x}{\sin ^3 x+\cos ^3 x} \mathrm{~d} x=\alpha \log _{\mathrm{e}}|1+\tan x|+\beta \log _{\mathrm{e}}\left|1-\tan x+\tan ^2 x\right|+\gamma \tan ^{-1}\left(\frac{2 \tan x-1}{\sqrt{3}}\right)+\mathrm{C}$, when C is constant of integration, then the value of $\displaystyle 18\left(\alpha+\beta+\gamma^2\right)$ is \_\_\_\_.
Official answer
3
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.