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JEE Main 2023 · 25 Jan · Shift 1

JEE Main 2023 Mathematics question on Indefinite Integration

Let f(x)=∫2x(x2+1)(x2+3) dxf(x) = \int \dfrac{2x}{(x^2+1)(x^2+3)}\, dx. If f(3)=12(log⁡e5−log⁡e6)f(3) = \dfrac{1}{2}(\log_e 5 - \log_e 6), then f(4)f(4) is equal to
  1. A.
    log⁡e17−log⁡e18\log_e 17 - \log_e 18
  2. B.
    12(log⁡e19−log⁡e17)\dfrac{1}{2}(\log_e 19 - \log_e 17)
  3. C.
    12(log⁡e17−log⁡e19)\dfrac{1}{2}(\log_e 17 - \log_e 19)
  4. D.
    log⁡e19−log⁡e20\log_e 19 - \log_e 20
Show answer

Correct option: C

[JEE Main 2023 · 25 Jan · Shift 1]

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