Evaluate the integrals in Exercises 1–14.
∫ (3 dx) / √(1 + 9x²)

In Exercises 69–80, determine whether the improper integral converges or diverges. If it converges, evaluate the integral.

∫₋∞⁰ x² e^(x³) dx

Moment about y-axis:

A thin plate of constant density δ = 1 occupies the region enclosed by the curve

y = 36/(2x + 3) and the line x = 3 in the first quadrant. Find the moment of the plate about the y-axis.

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

∫₂⁴ dt / [t√(t² − 4)]

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

∫ t² e^(4t) dt

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))

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)