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Question
Integrate the following with respect to x :
`(sin sqrt(x))/sqrt(x)`
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Solution
`int (sin sqrt(x))/sqrt(x) * "d"x`
Put `sqrt(x)` = u
`x^(1/2)` = u
`1/2 x^(1/2 - 1) "d"x` = du
`1/2 x^(- 1/2) "d"x` = du
`1/(2 x^(1/2)) "d"x` = du
`1/(2sqrt(x)) "d"x` = du
`1/sqrt(x) "d"x` = du
`int sin sqrt(x) * 1/sqrt(x) "d"x = int sin "u" 2 "du"`
= `2 int sin "u" "du"`
= `2 xx - cos "u" + "c"`
`int (sin sqrt(x))/sqrt(x) * "d"x = - 2 cos sqrt(x) + "c"`
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