Hey online, good to see you again. Step 1: Identify the integral. The integral to evaluate is: $$ \int \frac{x}{49-x^2} dx $$ Step 2: Use substitution. Let $u = 49 - x^2$. Differentiate $u$ with respect to $x$: $$ \frac{du}{dx} = -2x $$ Rearrange to express $x \, dx$ in terms of $du$: $$ du = -2x \, dx $$ $$ x \, dx = -\frac{1}{2} du $$ Step 3: Substitute into the integral. Substitute $u$ for $49-x^2$ and $-\frac{1}{2} du$ for $x \, dx$: $$ \int \frac{1}{u} \left(-\frac{1}{2}\right) du $$ $$ = -\frac{1}{2} \int \frac{1}{u} du $$ Step 4: Integrate with respect to $u$. The integral of $\frac{1}{u}$ is $\ln|u|$. $$ -\frac{1}{2} \int \frac{1}{u} du = -\frac{1}{2} \ln|u| + C $$ Step 5: Substitute back $u = 49 - x^2$. Replace $u$ with $49 - x^2$ to get the final answer in terms of $x$: $$ -\frac{1}{2} \ln|49 - x^2| + C $$ The evaluated integral is: $$ \boxed{-\frac{1}{2} \ln|49 - x^2| + C} $$ Send me the next one 📸