Please help me with the following questions. Thank you!

Express the integrand as a sum of partial fractions and evaluate the integrals. x + 5 dx 2x3 - 8X Rewrite the integrand as the sum of partial fractions. x +5 = 2x3 - 8x Evaluate the integrals. x + 5 dx = 2x3 - 8xA rectangular swimming pool is 42 ft wide by 75 ft long. The table gives depths (d) from x = O at the shallow end to the diving end. Use the Trapezoidal Rule with n = 15 to estimate the volume of the pool, 75 v: 42-d(x) dx. 35l40l45l50l55l60l65l70l75 10.3l10.7l11.1l11.5l11.8l12.1l12.5l12.8l13.1 The volume of the pool is ft3. (Round to the nearest integer as needed.) The accompanying tab e shows time-to-speed data for a particular car accelerating from rest to 125 mph. The car will travel ft by the time it reaches this speed. How far had the car traveled by the time it reached this speed? (Use trapezoids to estimate the area (Round the nal answer to three decimal places as needed. Round all intermediate values to ve under the velocity curve. Notice that intervals vary in length.) decimal places as needed.) Speed change Time (sec) Zero to 25 mph 2.2 35 mph 3.5 45 mph 5.1 55 mph 6.8 65 mph 9.0 75 mph 11.7 85 mph 14.5 95 mph 18.1 105 mph 23.0 1 15 mph 28.9 125 mph 40.1