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Question
Evaluate the following : `int cos sqrt(x).dx`
Solution
Let I = `int cos sqrt(x).dx`
Put `sqrt(x) = t`
∴ x = t2
∴ dx = 2t .dt
∴ I = `int(cost)2t.dt`
= `int 2t cos t.dt`
= `2t int cos.dt - int [d/dt (2t) int cos t.dt ].dt`
= `2tsint - int 2 sint.dt`
= 2t sin t + 2 cos t + c
= `2[sqrt(x)sinsqrt(x) + cos sqrt(x)] + c`.
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