Question

intregration cos log x upon x

Answer 1

Answer:

sin(logx) + c

Step-by-step explanation:

$\int\limits {\frac{cos(logx)}{x} } \, dx$    (1)

Let log x = t    (2)

Diff. w.r.t  x we get,

$\frac{1}{x}$ = $\frac{dx}{dt}$          

$\frac{1}{x}$* dx = dt   (3)

From (1) ,(2) ,(3)

$\int\limits {cos t} \, dt$

= sin t + c      (Since$\int\limits {cost} \, dt$ = sint )

Re substitution of t we get

= sin(logx) + c

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