10. Using the indicated techniques to evaluate the following integrals. Show work detail to support your solutions. Solving using other methods or with no detail is not acceptable. (a) Ii v9x2+4 (Trigonometric substitution) 2 (b) Jxzdx (Trigonometric substitution) l6 x J (c) I x2 In xdx (Integration by Parts) 11. Complete the square in the denominator, make appropriate substitution, and integrate the integral [x .7: + x+ 5 12. Find the partial fraction decomposition for the rational function and (u - 2)(u + 3) then evaluate the integral [+19% (u 2)(u + 3) 13. State whether the sequence converges or diverges. If it converges, nd its limit. 2 2 {mmzmm} n 14. Using the Integral Test to test the following series for convergence. Solving using other methods or with no detail is not acceptable. \" 1 \"=3 n(ln rt)2 15. Determine whether the following series converge or diverge. Indicate the test you use. (b) E "in" +2M2 2 16. Determine whether the series i [[1] [ %] ] converges or diverges. If it \"=0 converges, nd its sum. 1?. Determine whether the series 2( "=U\\/:1+3 absolutely, or diverges and give reasons for your conclusions. converges conditionally, or converges I! x 18. Find the interval of convergence for the power series 2 1 2 \"-0 n + cit-1 I 19. Use substitution method and a known power series to nd power series for Please express your answer in one sigma notation