11. Integrals of Inverse, Exponential, & Logarithmic Functions

Evaluate the indefinite integral.

${\int }_{}^{}\frac{e^{2\sqrt{x}}}{\sqrt{x}}dx$

Evaluate the integrals in Exercises 87–96.

87. ∫ 5ˣ dx

Evaluate the integrals in Exercises 31–78.

35. ∫sec²x e^(tan x)dx

Evaluate the integrals in Exercises 33–54.

53. ∫ (e^r / (1 + e^r)) dr

29–62. Integrals Evaluate the following integrals. Include absolute values only when needed.

∫₀ˡⁿ ² (e^{3x} − e^{−3x}) / (e^{3x} + e^{−3x}) dx

Evaluate the following integrals.

∫ e³ˣ/(eˣ - 1) dx

Evaluate the indefinite integral.

${\int }_{}^{}(\sqrt{x}-e^x)dx$

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

∫₋₁⁰ e^x / (e^x + e^(−x)) dx

Energy consumption On the first day of the year (t=0), a city uses electricity at a rate of 2000 MW. That rate is projected to increase at a rate of 1.3% per year.

b. Find the total energy (in MW-yr) used by the city over four full years beginning at t=0.

Oil consumption Starting in 2018 (t=0), the rate at which oil is consumed by a small country increases at a rate of 1.5%/yr, starting with an initial rate of 1.2 million barrels/yr.

c. How many years after 2018 will the amount of oil consumed since 2018 reach 10 million barrels?

Evaluate the integrals in Exercises 33–54.

∫ (e^(√r) / √r) dr

29–62. Integrals Evaluate the following integrals. Include absolute values only when needed.

∫₀^{π/2} 4^{sin x} cos x dx

Evaluate the indefinite integral.

${\int }_{}^{}(4e^x+\frac{1}{x^3})dx$

Evaluate the integrals in Exercises 33–54.

∫(from ln3 to ln2) (e^x) dx

Evaluate the integrals in Exercises 33–54.

∫(e^(3x) + 5e^(-x)) dx