### Integration of polynomial quotient and partial fractions

A example is shown whereby the velocity of an object is expressed as a quotient of two polynomials in time t. Such that velocity v = (t^2 + 18t + 21)/{(2t+1)*(t+4)^2} The problem asks to determine the displacement of the object after time t = 2.1s. The process requires the integration of the polynomial between the limit