Question

Find the general indefinite integral. (9-t) (4+t^2) dt

Answer 1

Best thing to do with this is to FOIL it out to a third degree polynomial then integrate it term by term.  In standard form the polynomial is $\int\limits {(36-4t+9t^2-t^3}) \, dt$.  We will use C as our constant of integration.  The integral now, assuming you know the rules for exponents, is $36t- \frac{4t^2}{2}+ \frac{9t^3}{3}- \frac{t^4}{4}+C$.  Simplifying that we would get $36t-2t^2+3t^3- \frac{1}{4}t^4+C$.  There you go!