Step 1 :Given the function: \(\frac{5x^4 - 7}{3x^3}\)
Step 2 :Simplify the function by dividing each term by \(3x^3\): \(\frac{5x^4}{3x^3} - \frac{7}{3x^3}\)
Step 3 :Further simplify: \(\frac{5}{3}x - \frac{7}{3x^3}\)
Step 4 :Find the integral of each term separately: \(\int\frac{5}{3}x dx - \int\frac{7}{3x^3} dx\)
Step 5 :Integrate: \(\frac{5}{6}x^2 + \frac{7}{6x^2} + C\)
Step 6 :\(\boxed{\frac{5x^2}{6} + \frac{7}{6x^2} + C}\) is the final answer