QJEEM19Ma6a31: JEE Main 2019 Mathematics - Class 12 JEEM19Ma6a31 Solution: The integral ∫ cos(log e x) dx is equal to : (where C is a…

Question

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The integral

\int

cos(log_e x) dx is equal to : (where C is a constant of integration)

Accepted Answer

I = \int \cos (ℓ n x) d x

I = \cos (\ln x) . x + \int \sin (ℓ n x) d x

I = \cos (ℓ n x) x + [\sin (ℓ n x) . x - \int \cos (ℓ n x) d x]

I = \frac{x}{2} [\sin (ℓ n x) + \cos (ℓ n x)] + C

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