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Evaluate the following integral: int1^3(...

Evaluate the following integral: `int_1^3(cos(logx))/x dx`

Text Solution

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Let `I=int_(1)^(3)(cos(logx))/(x)dx=int_(1)^(3)cos(logx).(1)/(x)dx`
Put log `x=t" "therefore" "(1)/(dx)dx=dt`
When `x=1, t = log 1=0`
When `x=3, t = log 3`
`therefore I=int_(0)^(log3) cost dt =[sin t]_(0)^(log3)`
`=sin(log3)-sin0 = sin (log3).`
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