Evaluate the integrals in Exercises 97–110.
101. ∫ (log₁₀x / x) dx

Evaluate the integrals in Exercises 31–78.

64. ∫(from 1 to e)(8ln3 log_3(θ))/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.

∫ dx / (x - √x)

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

Evaluate the integrals in Exercises 97–110.

103. ∫₁⁴ (ln 2 · log₂x / x) dx

Evaluate the integrals in Exercises 97–110.

107. ∫₀⁹ (2 log₁₀(x + 1) / (x + 1)) dx

Evaluate the integrals in Exercises 87–96.

95. ∫₂⁴ x^(2x) (1 + ln x) dx

Evaluate the integrals in Exercises 67–74 in terms of

b. natural logarithms.

71. ∫(from 1/5 to 3/13)dx/(x√(1-16x²))