Mathematics

The key is recognizing that the denominator $x$ is exactly the derivative of $\ln x$. Use substitution $u = \ln x$ so that $du = \frac{1}{x}\,dx$, transforming this into a much simpler integral involving $\cos u$. Once you integrate, remember to substitute back to express your answer in terms of $x$.

The key is recognizing that the denominator $x$ is exactly the derivative of $\ln x$. Use substitution $u = \ln x$ so that $du = \frac{1}{x}\,dx$, transforming this into a much simpler integral involving $\cos u$. Once you integrate, remember to substitute back to express your answer in terms of $x$.