int(cosx-cos2x)/(1-cosx)dx=?

Explanation:

Another Explanation (5): সমাধান: \[ \int \frac{\cos x - \cos 2x}{1 - \cos x} dx \] আমরা জানি, \(\cos 2x = 2\cos^2 x - 1\). সুতরাং, \[ \int \frac{\cos x - (2\cos^2 x - 1)}{1 - \cos x} dx = \int \frac{\cos x - 2\cos^2 x + 1}{1 - \cos x} dx \] এখন, লবকে সাজিয়ে লিখি: \[ \int \frac{1 + \cos x - 2\cos^2 x}{1 - \cos x} dx = \int \frac{(1 - \cos x)(1 + 2\cos x)}{1 - \cos x} dx \] সুতরাং, \[ \int (1 + 2\cos x) dx = \int 1 dx + 2\int \cos x dx = x + 2\sin x + c \] অতএব, উত্তর: \(x + 2\sin x + c\) 🎉