Evaluate $\int_{0}^{5} \frac{x}{4 x^{2}+5} d x$

Step 1 ：Evaluate \(\int_{0}^{5} \frac{x}{4 x^{2}+5} d x\)

Step 2 ：Use the method of partial fractions to decompose the integrand into simpler fractions

Step 3 ：Integrate the decomposed fractions

Step 4 ：\(\int_{0}^{5} \frac{x}{4 x^{2}+5} d x = -\frac{\log(5)}{8} + \frac{\log(105)}{8}\)

Step 5 ：\(\boxed{-\frac{\log(5)}{8} + \frac{\log(105)}{8}}\)