Question

integration of square root 1+cosx​

Answer 1

Step-by-step explanation:

$\sf \int \sqrt{1+cosx}dx \\ \\ \sf = \int \sqrt{\frac{{cos}^{2}\frac{x}{2}}{2}} dx \\ \\ \sf = \int \frac{1}{2} cos\frac{x}{2} dx \\ \\ \sf \frac{1}{2} \int cos\frac{x}{2} dx \\ \\ \sf = \frac{1}{2} (-sin\frac{x}{2})\frac{1}{1/2} \\ \\ \sf = - sin\frac{x}{2} + c$

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