The integrals in Exercises 1–34 converge. Evaluate the integrals without using tables.
∫₂⁴ dt / [t√(t² − 4)]

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.

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

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 1–44 are in no particular order. Evaluate each integral using any algebraic method, trigonometric identity, or substitution you think is appropriate.

∫ (dx / ((x - 2)√(x² - 4x + 3)))