\text{ If } \int (\frac{1}{x}+\frac{1}{x^3}) (23 \sqrt{3 x^{-24}+x^{-26}}) \dx =-\frac{\alpha}{3(\alpha+1)} (3 x^\beta+x^\gamma) ^{\frac{\alpha+1}{\alpha}}+C, x>0,(\alpha, \beta, \gamma \in Z) where C is the constant of integration, then \alpha+\beta+ \gamma is equal to \_\_\_\_ . [7 Apr 2025 Shift 2]

JEE Main 7 Apr 2025 Shift 2 Paper

Section: Mathematics

Question : 22 of 75

Marks: +1, -0

‌‌ If ‌∫(‌

+‌

)(23√3x−24+x−26)‌dx
‌=−‌

3(α+1)

(3xβ+xγ)‌

α+1

+C,x>0,(α,β,γ∈Z) where C is the constant of integration, then α+β+γ is equal to ____ .

[7 Apr 2025 Shift 2]

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