int(1-cos2x)/(1+cos2x)

Explanation:

Another Explanation (5): সমাধান: আমরা জানি, \(cos2x = 2cos^2x - 1 = 1 - 2sin^2x\)। অতএব, \[ \begin{aligned} \int \frac{1-cos2x}{1+cos2x} dx &= \int \frac{1-(1-2sin^2x)}{1+(2cos^2x-1)} dx \\ &= \int \frac{2sin^2x}{2cos^2x} dx \\ &= \int tan^2x dx \\ &= \int (sec^2x - 1) dx \\ &= \int sec^2x dx - \int 1 dx \\ &= tanx - x + C \end{aligned} \] সুতরাং, \(\int \frac{1-cos2x}{1+cos2x} dx = tanx - x + C\) 🥳 উত্তর: \(tanx - x\) 😊