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MCQMediumJEE Main 2026 · 24 January, Shift 1Indefinite Integrals

Mathematics Question from JEE Main 2026 · 24 January, Shift 1

Let f(t)=∫(1−sin⁡(log⁡et)1−cos⁡(log⁡et))dt,  t>1.f(t)=\int \left(\frac{1-\sin(\log_e t)}{1-\cos(\log_e t)}\right)dt,\; t>1. If f(eπ/2)=−eπ/2f(e^{\pi/2})=-e^{\pi/2} and f(eπ/4)=αeπ/4,f(e^{\pi/4})=\alpha e^{\pi/4}, then α\alpha equals

  • A

    −1+2-1+\sqrt{2}

  • B

    −1−22-1-2\sqrt{2}

  • C

    −1−2-1-\sqrt{2}

  • D

    1+21+\sqrt{2}

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