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MathsJEE Main 2 Apr 2026, Shift 2·Q19·MCQ·Easy–moderate

Indefinite Integration · Integration by partial fractions

Let f(x)=∫(16x+24x2+2x−15)dxf(x) = \displaystyle\int\left(\frac{16x + 24}{x^2 + 2x - 15}\right)dx. If f(4)=14log⁡e(3)f(4) = 14\log_e(3) and f(7)=log⁡e(2α⋅3β)f(7) = \log_e(2^{\alpha}\cdot3^{\beta}), α,β∈N\alpha, \beta \in \mathbb{N}, then α+β\alpha + \beta is equal to:
  1. (1)31
  2. (2)37
  3. (3)39
  4. (4)41

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