Indefinite Integration · Special integral of exponential form

Let

f(t) = \displaystyle\int\left(\dfrac{1 - \sin(\log_e t)}{1 - \cos(\log_e t)}\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

Video solution coming soon

We're animating every PYQ step by step. Subscribe to get them first.