I = ∫√(1+sin x)dx ∫ (cos x2+sinx2)dx =sinx21/2 cosx21/2+c=2 sin x2 2 cos x2+c ...

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Implicit Differentiation

Evaluate: ∫...

Question

Evaluate: $\int \sqrt{1 + s i n x} d x$

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Solution

$I =$ $\int \sqrt{1 + s i n x} d x$

$\int (c o s \frac{x}{2} + s i n \frac{x}{2}) d x$

$= \frac{s i n \frac{x}{2}}{1 / 2} - \frac{c o s \frac{x}{2}}{1 / 2} + c = 2 s i n \frac{x}{2} - 2 c o s \frac{x}{2} + c$

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