1. Find the partial fraction decomposition for the rational function x2 - x+5 x3+x 2. Use the partial fraction decomposition of the function to evaluate the integral x + 5 x(x - 1)2 dx 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. dx (a) Vx2 +9 1 (b ) dx x2 V16-x2 Font (c) X dx Vx2 -4 4. First complete the square, make the appropriate substitutions, and then evaluate the integral: -dx Vx2 - 2x +5 5. Evaluate each of the following integrals, using the given substitution or identity. Solutions using other methods are not acceptable (a) [cos' xsin xdx (substitution u = sin x ) (b) [" tan' x sec* xdx (substitution u = tan x ) (c) [ sin(5x) sin(3x) dx ( sin( A) sin( B) = = [cos(A - B) - cos( A + B)]) . N (d) [ cos(6x) cos(4x)dx (cos( A) cos(B) = =[cos(A - B) + cos( A + B)])