$\displaystyle \int \dfrac{1}{x \cos^2 (1 + \log x)} dx = ?$
Solution
$\displaystyle \int \dfrac{1}{x \cos^2 (1 + \log x)} dx$
$1 + \log x = 7$ रखने पर
$\dfrac{dx}{x} = z$
$\therefore \displaystyle \int \dfrac{dz}{\cos^2 z} = \displaystyle \int \sec^2 z dz$
$= \tan z + c = \tan (1 + log x) + c$