11. Integrals of Inverse, Exponential, & Logarithmic Functions

Evaluate the integrals in Exercises 33–54.

∫ (e^(1/x) / x²) dx

The integrals in Exercises 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.

∫ ((2ˣ - 1) / 3ˣ) 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.

∫ e^(ln√x) dx

Find the area of $f\left(x\right)=3+e^{2x}$ from $x=0$ to $x=2$.

Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.

∫ e^(-3t) sin(4t) dt

Evaluate the integrals in Exercises 87–96.

89. ∫₀¹ 2^(−θ) dθ

The integrals in Exercises 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.

∫ e^(z + eᶻ) dz

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

∫ (e^x + e^(3x)) / e^(2x) 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.

c. Find a function that gives the total energy used (in MW-yr) between t=0 and any future time t>0.

37–56. Integrals Evaluate each integral.

∫ eˣ/(36 – e²ˣ), x < ln 6

Evaluate ∫ 4ˣ dx.

Evaluate the integrals in Exercises 87–96.

91. ∫₁^(√2) x·2^(x²) dx

2–9. Integrals Evaluate the following integrals.

∫ (eˣ / (4eˣ + 6)) dx

The integrals in Exercises 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.

∫ (2^(√y) dy) / 2√y

Evaluate the integrals in Exercises 33–54.

51. ∫ from ln(π/6) to ln(π/2) 2e^v cos(e^v) dv