NVAMediumJEE Main 2023 · 30 January, Shift 2Indefinite Integrals

Mathematics Question from JEE Main 2023 · 30 January, Shift 2

If

∫sec⁡2x−1 dx=αlog⁡e∣cos⁡2x+β+cos⁡2x(1+cos⁡1βx)∣+constant\int \sqrt{\sec 2x - 1} \, dx = \alpha \log_e \left| \cos 2x + \beta + \sqrt{\cos 2x \left( 1 + \cos \frac{1}{\beta} x \right)} \right| + \text{constant}

then β−α\beta - \alpha is equal to _____

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