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Integration of Exponential, Logarithmic, and Hyperbolic Functions: Get Stronger Answer Key
Integrals, Exponential Functions, and Logarithms
- 1x
- −1x(lnx)2
- ln(x+1)+C
- ln(x)+1
- cot(x)
- 7x
- csc(x)secx
- −2tanx
- 12ln(53)
- 2−12ln(5)
- 1ln(2)−1
- 12ln(2)
- 13(lnx)3
- 2x3√x2+1√x2−1
- x−2−(1/x)(lnx−1)
- exe−1
- 1
- −1x2
- π−ln(2)
- 1x
- e5−6units2
- ln(4)−1units2
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Exponential Growth and Decay
- True
- False; k=ln(2)t
- 20 hours
- No. The relic is approximately 871 years old.
- 71.92 years
- 5 days 6 hours 27 minutes
- 12
- 8.618%
- $6766.76
- 9 hours 13 minutes
- 239,179 years
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- P′(t)=43e0.01604t. The population is always increasing.
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- The population reaches 10 billion people in 2027.
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- P′(t)=2.259e0.06407t. The population is always increasing.
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Calculus of the Hyperbolic Functions
- ex and e−x
- Answers may vary
- Answers may vary
- Answers may vary
- 3sinh(3x+1)
- −tanh(x)sech(x)
- 4cosh(x)sinh(x)
- xsech2(√x2+1)√x2+1
- 6sinh5(x)cosh(x)
- 12sinh(2x+1)+C
- 12sinh2(x2)+C
- 13cosh3(x)+C
- ln(1+cosh(x))+C]
- cosh(x)+sinh(x)+C
- 41−16x2
- sinh(x)√cosh2(x)+1
- −csc(x)
- −1(x2−1)tanh−1(x)
- 1atanh−1(xa)+C
- √x2+1+C
- cosh−1(ex)+C
- −0.521095
- 10
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