Let $f\left(t\right)=\int \left(\frac{1−\sin \left({\log }_{e}t\right)}{1−\cos \left({\log }_{e}t\right)}\right)dt,t1.$ If $f\left({e}^{\pi /2}\right)=−{e}^{\pi /2}$ and $f\left({e}^{\pi /4}\right)=\alpha {e}^{\pi /4},$ then $\alpha$ equals [JEE Main 2026, 24 Jan (Shift 1)]

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Let $f\left(t\right)=\int \left(\frac{1−\sin \left({\log }_{e}t\right)}{1−\cos \left({\log }_{e}t\right)}\right)dt,t>1.$ If $f\left({e}^{\pi /2}\right)=−{e}^{\pi /2}$ and $f\left({e}^{\pi /4}\right)=\alpha {e}^{\pi /4},$ then $\alpha$ equals [JEE Main 2026, 24 Jan (Shift 1)]

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Let \(f\left(t\right)=\int \left(\frac{1−\sin \left({\log }_{e}t\right)}{1−\cos \left({\log }_{e}t\right)}\right)dt,t>1.…

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