Question

Evaluate:

$\int [\sin \left(\log x\right)+\cos \left(\log x\right)]dx$

Answer 1

$I=\int \sin \left(\log x\right)+\cos \left(\log x\right)dx$

$\log x=t$

$x=e^t$

$dx=e^{t}dt$

$\therefore I=\int (\sin t+\cos t)e^{t}dt$

$=\int d\left(\sin t{e}^t\right)$

$=\sin t{e}^t+c$

$=x\sin \left(\log x\right)+c$