The integral [ , ]cos(loge x) dx is equal to : (where C is a constant of integration)

Question

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

Accepted Answer

$${\rm I} = \int {\cos \left( {\ell nx} \right)} dx$$

$${\rm I} = \cos (\ln x).x + \int {\sin \left( {\ell nx} \right)dx} $$

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

$${\rm I} = {x \over 2}\left[ {\sin \left( {\ell nx} \right) + \cos \left( {\ell nx} \right)} \right] + C$$

Solutions · 1