Question

Evaluate: $\int \sqrt{1+sinx}dx$

Answer 1

$\int \sqrt{1+sinx}dx$ Replace $1\to si{n}^{2}xco{s}^{2}x$

$=\int \sqrt{si{n}^{2}x+co{s}^{2}x+2sin\frac{x}{2}}dx$ (using submultiple angle formula)

$=\int \sqrt{(sinx+cosx{)}^2}dx$

$=\int (sinx+cosx)dx$

$=-cosx+sinx+c$

Where c is the constant of integration.