UIZ # 5 Problems (An answer, even if \"correct\" but lacking work, will NOT receive full credit!) 1. Find the partial fraction decomposition for the rational function 2x2 x 4 x3 4x 2. Use the partial fraction decomposition of the functions to evaluate the integral . Solving using a formula is not acceptable. x 5 ( x 1)( x 2)dx 3. Evaluate each of the following integrals, using a trigonometric substitution. Do not forget the back substitution. Solving using other methods is not acceptable. (a) dx 4 x 2 1 (b) 1 x 2 x 2 9dx x 16 x 2 dx (c) 4. First complete the square, make the appropriate substitutions, and evaluate the integral: 1 x 2 2 x 5 dx 5. Evaluate each of the following integrals, using the hints. (a) (b) 3 6 cos x sin xdx /4 0 (Hints: substitution (Hints: substitution 3 4 tan x sec xdx (c) (Hints: sin( 5x) sin( 3x)dx (d) (Hints: cos(6 x) cos(4 x)dx u sin x u tan x & identity cos 2 x sin 2 x 1 & identity ) sec 2 x 1 tan 2 x 1 sin( A) sin( B ) [cos( A B ) cos( A B )] 2 1 cos( A) cos( B ) [cos( A B ) cos( A B )] 2 ) ) )