Evaluate the integrals in Exercises 31–78.
64. ∫(from 1 to e)(8ln3 log_3(θ))/θ dθ

Evaluate the integrals in Exercises 39–56.

55. ∫dx/(2√x + 2x)

Evaluate the integrals in Exercises 97–110.

109. ∫ (dx / (x log₁₀x))

Evaluate the integrals in Exercises 31–78.

45. ∫(ln x)^(-3)/x dx

Evaluate the integrals in Exercises 31–78.

61. ∫(from 1 to 3)(ln(v+1))²/(v+1) dv

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.

∫ dx / (x - √x)

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.

∫ (x + 2√(x - 1)) / (2x√(x - 1)) dx

Use any method to evaluate the integrals in Exercises 15–38. Most will require trigonometric substitutions, but some can be evaluated by other methods.

∫ (x dx) / (25 + 4x²)

In Exercises 39–48, use an appropriate substitution and then a trigonometric substitution to evaluate the integrals.

∫ √(1 - (ln x)²) / (x ln x) dx