Mathematics

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


SOLUTION
$$\int \sqrt{1+sin x}dx$$      Replace $$1\rightarrow sin^{2}x cos^{2}x$$
$$= \int \sqrt{sin^{2}x+cos^{2}x+2 sin\frac{x}{2}}dx$$    (using submultiple angle formula)
$$=\int \sqrt{(sin x+cos x)^{2}}dx$$
$$ =\int (sin x+cos x)dx$$
$$=-cos x+sin x+c$$
Where c is the constant of integration.
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Subjective Medium Published on 17th 09, 2020
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