Evaluate $\int \frac{\cos (\ln x)}{x} d x$ .
A) $-\sin (\ln x)+C$
B) $\sin (\ln x)+C$
C) $\frac{-\sin (\ln x)}{x}+C$
D) $\frac{2 \sin (\ln x)}{x^{2}}+C$

Question

Quizplus · Accepted Answer

This integral can be solved by recognizing it as an integral involving a composition of functions, specifically with the substitution $u = \ln(x)$, which implies $du = \frac{1}{x}dx$. Substituting these into the integral gives $\int \cos(u) du$, which integrates to $\sin(u) + C$. Reverting back to the original variable, $u = \ln(x)$, gives $\sin(\ln(x)) + C$.

Evaluate ∫cos⁡(ln⁡x)xdx\int \frac{\cos (\ln x)}{x} d x∫xcos(lnx)​dx A) −sin⁡(ln⁡x)+C-\sin (\ln x)+C−sin(lnx)+C

Evaluate $\int \frac{\cos (\ln x)}{x} d x$
A) $-\sin (\ln x)+C$