_ ^ [ ( x) + ( x)] ;dx =

MCQ

$\int_{}^{} {[\sin (\log x) + \cos (\log x)]} \;dx = $

A
$x\cos (\log x) + c$
B
$\sin (\log x) + c$
C
$\cos (\log x) + c$
✓
$x\sin (\log x) + c$

✓

Answer

Correct option: D.

$x\sin (\log x) + c$

d
(d) $\int_{}^{} {\sin (\log x)\,dx} + \int_{}^{} {\cos (\log x)\,dx} $
$ = x\sin (\log x) - \int_{}^{} {\frac{{x\cos (\log x)}}{x}} \,dx + \int_{}^{} {\cos (\log x)\,dx + c} $
$ = x\sin (\log x) + c.$

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