QUIZ # 5 Problems 1. Find the partial fraction decomposition for the rational function x2 x + 5 x3 + :r 2. Use the partial fraction decommsition of the function to evaluate the integral I :r + 5 _d:r xtfx 1)2 Solving using a formula is not acceptable. 3. Evaluate each of the following integrals, using a trigonometric substitution. Do not forget the back substitution. Solving using other methods is not acceptable. 4. First complete the square, make the appropriate substitutions, and then evaluate the integral: 14v xix: 2.r+5 5. Evaluate each of the following integrals, using the given substitution or identity. Solutions using other methods are not acceptable. (a) Icos3 xsin nix (substitution at = sinx) (b) :MtanEl xsecd xdx (substitution at = tanx) (c) J-sin(5x) sin(3.r}d.r (sin{A) sin(B) = %[cos(A B) cos(A + B)]) (d) Icosix} cos(4x)dx (cos{A) cos(B) = %[cos(A B) + cos{A + B)])