### Problem 7: **Objective:** Evaluate the integral \[ \int \frac{x^4 + 3x^2}{x^2 - 1} \, dx \] **Instructions:** Simplify and solve the integral using appropriate calculus techniques, such as polynomial long division or partial fraction decomposition. Ensure that all steps are clearly shown and justified as part of the solution process.

I need some explanation on these 3 problems.

I am lost on what to do. I've tried to list what I know, but I got confused and have no leads. I'm working on Problem 3. Pleases help and show steps how to work out problem.

A tortoise and hare are competing in a 400-meter race. The arrogant hare gives the tortoise a 220-meter head start. When the start gun is fired, the hare begins running at a constant speed of 3.5 meters per second and the tortoise begins crawling at constant speed of 1.5 meters per second. Take out a piece of paper and read the above problem context again. You will prepare your written work and solutions on your own paper and upload it and the end of this question. Complete the problem solving process by: i. reading and re-reading the problem to identify the quantities in the situation; ii. making a drawing to represent the relevant quantities in the situation; iii. and defining the variable t to represent the number of seconds since the start of the race. a. Define a function f to determine the distance of the tortoise from the finish line in terms of the number of seconds, t, since the start of the race. Preview Solve f(t) = 0 and describe what your solution represents. t = Preview…