Use the properties of the integrals to rewrite the integral as the sum of the individual integral. cinc t In (t + 9) dt +² - Ince = 2 Submit In(t + 9) Apply the basic integration rule and the log rule. Itin = ¼[/tdt-f t dt- 2 2 31/12/20 = In(t + 9) + / -1² + t In(t + 9) dt In(t + 9) Skip (you cannot come back) dt + +81 In 162 In t + 81 1] + C 1+C + C dt

Solve integral

Sand is being dumped from a hopper railcar at a rate of 40 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal to each other (both are growing larger as more sand is dumped). How fast is the base diameter increasing when the base is 18 feet long? Round your answer to three decimal places. ft/min

Let f(x, y) = xy² and r(t) = (¹/1²,t³). Calculate Vf. (Use symbolic notation and fractions where needed. Express numbers in exact form. Give your answer in the form (*, *). ) Vf= Calculate r' (t). (Use symbolic notation and fractions where needed. Express numbers in exact form. Give your answer in the form (*, *). ) r' (t) = Use the Chain Rule for Paths to evaluateƒ(r(t)) at t = 1.5. (Use decimal notation. Give your answer to three decimal places.) d dt - ƒ(r(1.5)) = = Use the Chain Rule for Paths to evaluate ƒ(r(t)) at t = -1.7. (Use decimal notation. Give your answer to three decimal places.) d dt d f(r(-1.7)) =