In Exercises 27–40, use a substitution to change the integral into one you can find in the table. Then evaluate the integral.
∫ dt / (tan(t)√4 - sin^2(t))

The integrals in Exercises 1–34 converge. Evaluate the integrals without using tables.

∫₂⁴ dt / [t√(t² − 4)]

Evaluate the integrals in Exercises 1–14.

∫ (3 dx) / √(1 + 9x²)

Evaluate the integrals in Exercises 1–24 using integration by parts.

∫ t² e^(4t) dt

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

∫ dx / (1 + x²)

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

∫ √(x) / (1 - x³) dx (Hint: Let u = x³/2)

92. Evaluate ∫ from 3 to ∞ [ dx / (x √(x² - 9))]