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Question

Mathematics Question on integral

∫[sin(log x)+cos(log x)]dx\int\left[sin \left(log\,x\right)+cos\left(log\,x\right)\right]dx is equal to

A

x cos(log x)+cx\, cos (log\,x)+c

B

cos(log x)+ccos (log\,x)+c

C

x sin(log x)+cx\, sin (log\,x)+c

D

sin(log x)+csin (log\,x)+c

Answer

x sin(log x)+cx\, sin (log\,x)+c

Explanation

Solution

∫[sin⁡(log⁡x)+cos⁡(log⁡x)]dx\int[\sin (\log x)+\cos (\log x)] d x =∫ddxxsin⁡(log⁡x)dx=\int \frac{d}{d x}\\{x \sin (\log x)\\} d x =xsin⁡(log⁡x)+c=x \sin (\log x)+c