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Question
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Solution
`intsqrt(1 + sin 5x).dx`
= `intsqrt(sin^2 (5x)/2 + cos^2 (5x)/2 + 2sin (5x)/2 cos (5x)/2) dx`
= `intsqrt((cos (5x)/2 + sin (5x)/2)^2) dx`
= `int(cos (5x)/2 + sin (5x)/2) dx`
= `intcos (5x)/2 dx + sin (5x)/2 dx`
= `(sin (5x)/2)/(5/2) - (cos (5x)/2)/(5/2) + "c"`
∴ I = `2/5 (sin (5x)/2-cos (5x)/2) + "c"`
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