Question

Evaluate : `int_1^3 (cos(logx))/x*dx`

Answer 1

Let I = `int_1^3 (cos(logx))/x*dx`

= `int_1^3 cos(logx)*1/x*dx`
Put log x = t

∴ `(1)/x*dx` = dt
When x = 1, t = log 1 = 0
When x = 3, t = log 3

∴ I = `int_0^log3  cos t *dt = [sint]_0^log3`

= sin (log 3) - sin 0
= sin (log 3).