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 / ((2x + 1)√(4x + 4x²)))

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

∫₁^∞ dx / x^1.001

Evaluate the integrals in Exercises 33–52.

∫ cot³(t) csc⁴(t) dt

Evaluate the integrals in Exercises 23–32.

∫_{π/2}^{3π/4} √(1 - sin(2x)) dx

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.

∫ (2^(√y) dy) / 2√y

Expand the quotients in Exercises 1–8 by partial fractions.

z / (z³ - z² - 6z)

Exercises 83–86 are about the infinite region in the first quadrant between the curve y = e^(-x) and the x-axis.

83. Find the area of the region.