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Question
Evaluate the following:
`int sqrt(1 + sinx)"d"x`
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Solution
I = `int sqrt(1 + sinx)"d"x`
= `int sqrt(sin^2 x/2 + cos^2 x/2 + 2 sin x/2 cos x/2) "d"x`
= `int sqrt((sin x/2 + cos x/2)^2) "d"x`
= `int (sin x/2 + cos x/2) "d"x`
= `1/(1/2)(- cos x/2 + sin x/2) + "C"`
= `2(- cos x/2 + sin x/2) + "C"`
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