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Integration of Exponential, Logarithmic, and Hyperbolic Functions: Get Stronger Answer Key

Integrals, Exponential Functions, and Logarithms

  1. 1x
  2. 1x(lnx)2
  3. ln(x+1)+C
  4. ln(x)+1
  5. cot(x)
  6. 7x
  7. csc(x)secx
  8. 2tanx
  9. 12ln(53)
  10. 212ln(5)
  11. 1ln(2)1
  12. 12ln(2)
  13. 13(lnx)3
  14. 2x3x2+1x21
  15. x2(1/x)(lnx1)
  16. exe1
  17. 1
  18. 1x2
  19. πln(2)
  20. 1x
  21. e56units2
  22. ln(4)1units2
  23.  
  24.  
  25.  
  26.  
  27.  

Exponential Growth and Decay

  1. True
  2. False; k=ln(2)t
  3. 20 hours
  4. No. The relic is approximately 871 years old.
  5. 71.92 years
  6. 5 days 6 hours 27 minutes
  7. 12
  8. 8.618%
  9. $6766.76
  10. 9 hours 13 minutes
  11. 239,179 years
  12.  
  13. P(t)=43e0.01604t. The population is always increasing.
  14.  
  15. The population reaches 10 billion people in 2027.
  16.  
  17. P(t)=2.259e0.06407t. The population is always increasing.
  18.  

Calculus of the Hyperbolic Functions

  1. ex and ex
  2. Answers may vary
  3. Answers may vary
  4. Answers may vary
  5. 3sinh(3x+1)
  6. tanh(x)sech(x)
  7. 4cosh(x)sinh(x)
  8. xsech2(x2+1)x2+1
  9. 6sinh5(x)cosh(x)
  10. 12sinh(2x+1)+C
  11. 12sinh2(x2)+C
  12. 13cosh3(x)+C
  13. ln(1+cosh(x))+C]
  14. cosh(x)+sinh(x)+C
  15. 4116x2
  16. sinh(x)cosh2(x)+1
  17. csc(x)
  18. 1(x21)tanh1(x)
  19. 1atanh1(xa)+C
  20. x2+1+C
  21. cosh1(ex)+C
  22. 0.521095
  23. 10
  24.  
  25.  
  26.