The integral cos ⁡ ( log_ex ) dx is equal to : (where C is a constant of integration)

Question

Accepted Answer

Correct answer: C. (c) Let the integral I= cos ⁡ ( ln ⁡x ) dx ⇒I= cos ⁡ ( ln ⁡x ) x- - sin ⁡ ( ln ⁡x )x xdx =x cos ⁡ ( ln ⁡x )+ sin ⁡ ( ln ⁡x ) dx =x cos ⁡ ( ln ⁡x )+ sin ⁡ ( ln ⁡x ) x- cos ⁡ ( ln ⁡x )x xdx =x cos ⁡ ( ln ⁡x )+ sin ⁡ ( ln ⁡x ) x-I ⇒2I=x ( cos ⁡ ( ln ⁡x )+ sin ⁡ ( ln ⁡x ) )+C ⇒I= x2 [ cos ⁡ ( ln ⁡x )+ sin ⁡ ( ln ⁡x ) ]+C

$The integral \int cos (log_{e} x) dx is equal to : (where C is a constant of integration)$

Solution

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