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7.7 Assess Your Understanding

Printed Page 523

523

Skill Building

In Problems 1–16, find each integral using the Table of Integrals found at the back of the book.

  1. e2xcosxdx

15e2x(2cosx+sinx)+C

  1. e5x+1sin(2x+3)dx

  1. x4x+3dx

120(2x1)(3+4x)3/2+C

  1. dx(x21)3/2

  1. (x+1)4x+5dx

6x+560(4x+5)3/2+C

  1. dx[(2x+3)21]3/2

  1. dxx4x+6

66ln|6+4x66+4x+6|+C

  1. dxx8+x

  1. 4x+6xdx

26+4x+6ln|6+4x66+4x+6|+C

  1. 8+xx2dx

  1. x3(lnx)2dx

x4(lnx)24x4lnx8+x432+C

  1. x3(lnx)2dx

  1. sin1(2x)dx

xsin1(2x)+1214x2+C

  1. tan1(3x)dx

  1. 21x33xx2dx

1358sin113924

  1. e11x2x2+2dx

In Problems 17–32:

  1. (a) Redo Problems 1-16 using a CAS.
  2. (b) Compare the result to the answer obtained using a Table of Integrals.
  3. (c) If the results are different, verify that they are equivalent.
  1. e2xcosxdx

  1. (a) e2x5(sinx+2cosx)+C
  2. (b) See Student Solutions Manual.
  3. (c) See Student Solutions Manual.
  1. x4x+3dx

  1. (a) 2x120(4x+3)3/2+C
  2. (b) See Student Solutions Manual.
  3. (c) See Student Solutions Manual.
  1. (x+1)4x+5dx

  1. (a) 6x+560(4x+5)3/2+C
  2. (b) See Student Solutions Manual.
  3. (c) See Student Solutions Manual.
  1. dxx4x+6

  1. (a) 136tanh1(4x+666)+C
  2. (b) See Student Solutions Manual.
  3. (c) See Student Solutions Manual.
  1. 4x+6xdx

  1. (a) 24x+626tanh12x3+1+C
  2. (b) See Student Solutions Manual.
  3. (c) See Student Solutions Manual.
  1. x3(lnx)2dx

  1. (a) 132x4(8ln2x4lnx+1)+C
  2. (b) See Student Solutions Manual.
  3. (c) See Student Solutions Manual.
  1. sin1(2x)dx

  1. (a) 1214x2+xsin1(2x)+C
  2. (b) See Student Solutions Manual.
  3. (c) See Student Solutions Manual.
  1. 21x33xx2dx

  1. (a) 924+1358sin113
  2. (b) See Student Solutions Manual.
  3. (c) See Student Solutions Manual.

In Problems 33–38, use a CAS to investigate whether each indefinite integral can be expressed using elementary functions.

  1. 1+x3dx

No

  1. 1+sinxdx

  1. ex2dx

No

  1. cosxxdx

  1. xtanxdx

No

  1. 1+exdx