Question

question given that $f(x)=int_{0}^{x}\frac{ln t}{2 + t^{2}}dt$, what is $f(x)$? (do not include \$f(x)=$\ in your answer.) provide your answer below:

Explanation:

Step1: Apply fundamental theorem of calculus

If $F(x)=\int_{a}^{x}f(t)dt$, then $F^{\prime}(x) = f(x)$. Here $a = 0$ and $f(t)=\frac{\ln t}{2 + t^{2}}$.

Step2: Find the derivative

By the fundamental theorem of calculus, $F^{\prime}(x)=\frac{\ln x}{2 + x^{2}}$.

Answer:

$\frac{\ln x}{2 + x^{2}}$