Evaluate, \( \int_{1}^{5}\left(\frac{3 x}{x^{3}}\right) d x \)

Calculate the integral \( \int_{1}^{5}\left(\frac{3x}{x^{3}}\right)dx \). Evaluate the integral by following steps: - step0: Evaluate using formulas and rules: \(\int_{1}^{5} \frac{3x}{x^{3}} dx\) - step1: Divide the terms: \(\int_{1}^{5} \frac{3}{x^{2}} dx\) - step2: Evaluate the integral: \(\int \frac{3}{x^{2}} dx\) - step3: Rewrite the expression: \(\int 3\times \frac{1}{x^{2}} dx\) - step4: Use properties of integrals: \(3\times \int \frac{1}{x^{2}} dx\) - step5: Evaluate the integral: \(3\times \frac{x^{-2+1}}{-2+1}\) - step6: Simplify: \(3\left(-\frac{1}{x}\right)\) - step7: Multiply the terms: \(-3\times \frac{1}{x}\) - step8: Multiply the terms: \(-\frac{3}{x}\) - step9: Return the limits: \(\left(-\frac{3}{x}\right)\bigg |_{1}^{5}\) - step10: Calculate the value: \(\frac{12}{5}\) The integral of \( \frac{3x}{x^3} \) from 1 to 5 is \( \frac{12}{5} \) or \( 2\frac{2}{5} \) or 2.4.