Use the formula ∫ f⁻¹(x) dx = x f⁻¹(x) - ∫ f(y) dy, y = f⁻¹(x)
To evaluate the integrals in Exercises 77-80. Express your answers in terms of x.
∫ arctan x dx

Evaluate the integrals in Exercises 23–32.

∫₀^π √(1 - cos²(θ)) dθ

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

∫₀⁴ dx / √(4 − x)

Evaluate the integrals in Exercises 1–22.

∫₀^π 8cos⁴(2πx) dx

Solve the initial value problems in Exercises 67–70 for x as a function of t.

(3t⁴ + 4t² + 1) (dx/dt) = 2√3, x(1) = -π√3/4

Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.

∫ x arctan(x) dx

Finding volume: Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^x, and the line x = ln(2) about the line x = ln(2).