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`intsqrt(1+sinx)dx`

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`intsqrt(1+sinx)dx=intsqrt("sin"^(2)(x)/(2)+"cos"^(2)(x)/(2)+2"sin"(x)/(2)"cos"(x)/(2))dx`
`=int("sin"(x)/(2)+"cos"(x)/(2))dx=int"sin"(x)/(2)dx+int"cos"(x)/(2)dx`
`=-2"cos"(x)/(2)+2"sin"(x)/(2)+C`.
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