JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumUnclassified (maths)If ∫(1x+1x3)(3x−24+x−26)dx\int \left( \frac{1}{x} + \frac{1}{x^3} \right) \left( \sqrt{3x^{-24} + x^{-26}} \right) dx∫(x1+x31)(3x−24+x−26)dx is equal to α3(α+1)(3xβ+xγ)α+1α+C, x>0,\frac{\alpha}{3(\alpha + 1)} \left(3x^{\beta} + x^{\gamma}\right)^{\frac{\alpha + 1}{\alpha}} + C,\ x > 0,3(α+1)α(3xβ+xγ)αα+1+C, x>0, where α,β,γ∈Z\alpha, \beta, \gamma \in \mathbb{Z}α,β,γ∈Z, and CCC is the constant of integration, then α+β+γ\alpha + \beta + \gammaα+β+γ is equal to:Your answerInteger or decimalCheckStep-by-step hintSkip · show solution
