Question

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

• A. $\frac{x}{2}\left[\sin \left({\log }_{e}x\right)-\cos \left({\log }_{e}x\right)+C\right]$
• B. $\frac{x}{2}\left[\cos \left({\log }_{e}x\right)+\sin \left({\log }_{e}x\right)\right]+C$
• C. $x[\cos ({\log }_{e}x)+\sin ({\log }_{e}x)]+C$
• D. $x[\cos ({\log }_{e}x)-\sin ({\log }_{e}x)]+C$

Answer 1

Answer: (B)

$I=\int \cos \left(\ell nx\right)dx$
$I=\cos \left(lnx\right).x+\int \sin \left(\ell nx\right)dx$
$\cos \left(\ell nx\right)x+\left[\sin \left(\ell nx\right).x-\int \cos \left(\ell nx\right)dx\right]$
$I=\frac{x}{2}\left[\sin \left(\ell nx\right)+\cos \left(\ell nx\right)\right]+C$