Evaluate the integrals in Exercises 67–74 in terms of
b. natural logarithms.
67. ∫(from 0 to 2√3)dx/√(4+x²)

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

∫ (e^{t} dt) / ((1 + e^{2t})^{3/2}) from ln(3/4) to ln(4/3)

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

∫₀^(π/3) tan³x·sec²x 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.

∫₀³ (x + 2)√(x + 1) dx

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

∫ dy / (y√(1 + (ln y)²)) from 1 to e

Evaluate the integrals in Exercises 67–74 in terms of

b. natural logarithms.

69. ∫(from 5/4 to 2)dx/(1-x²)

135. Evaluate ∫₀^(π/2) (sin x) / (sin x + cos x) dx in two ways:

(a) By evaluating ∫ (sin x) / (sin x + cos x) dx, then using the Evaluation Theorem.

Evaluate the integrals in Exercises 1–22.

∫₀^π 8cos⁴(2πx) dx

Evaluate the integrals in Exercises 39–56.

43. ∫(from 0 to π)(sin t)/(2 - cos t) dt