11. Integrals of Inverse, Exponential, & Logarithmic Functions

2–9. Integrals Evaluate the following integrals.

∫ (x + 4) / (x² + 8x + 25) dx

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. Assume x > 0 and y > 0.

e. The area under the curve y = 1/x and the x-axis on the interval [1, e] is 1.

49–63. {Use of Tech} Integrating with a CAS Use a computer algebra system to evaluate the following integrals. Find both an exact result and an approximate result for each definite integral. Assume a is a positive real number.

61. ∫₀¹ (ln x) ln(1 + x) dx