Please help me solve these questions

Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and then evaluate the integral. y4+2y2_1 d y~ +2y Perform long division on the given integrand and write the proper fraction as a sum of partial fractions. oy (Simplify your answer. Use integers or fractions for any numbers in the expression.) v+ 2y -1 ) Evaluate the integral. 3 dx 3/2 X - X 3 dx = 3/2 X VXUse any method to evaluate the integral. Evaluate the indefinite integral. dx IH=D \fFind the volume of the solid generated by revolving the 5-7 + shaded region about the x-axis. 13 The curve is y = - -; X, = 1.75, x, = 10.5. X 1 13x - x2 12 The volume of the solid is (Type an exact answer, using it as needed.)In a sufficiently large population, the number of people x who have a certain piece of information can be treated as a (a) x= D differentiable function of time t, and the rate at which the information spreads, %, is assumed to be proportional to the number of people who have the information times the number of people who do not. This leads to the equation following equation d_x =kx(N - x), where N is the number of people in the population. Suppose tis in days, k= dt and two people share the information at time t=0 in a population of N =750 people. 250 (a) Find x as a function of t. (b) When will half the population have heard the information? (This is when the rumor will be spreading the fastest.)