intcos^2(x/2)dx=? 

Explanation:

Another Explanation (5): সমাধান: \( \int \cos^2\left(\frac{x}{2}\right) dx \) আমরা জানি, \( \cos 2\theta = 2\cos^2 \theta - 1 \). সুতরাং, \( \cos^2 \theta = \frac{1 + \cos 2\theta}{2} \). এখানে, \( \theta = \frac{x}{2} \). সুতরাং, \[ \cos^2 \left(\frac{x}{2}\right) = \frac{1 + \cos x}{2} \] তাহলে, \[ \int \cos^2\left(\frac{x}{2}\right) dx = \int \frac{1 + \cos x}{2} dx \] \[ = \frac{1}{2} \int (1 + \cos x) dx \] \[ = \frac{1}{2} \left[ \int 1 dx + \int \cos x dx \right] \] \[ = \frac{1}{2} \left[ x + \sin x \right] + C \] \[ = \frac{1}{2} (x + \sin x) + C \] সুতরাং, \( \int \cos^2\left(\frac{x}{2}\right) dx = \frac{1}{2} (x + \sin x) + C \) 🥳🥳