7. Antiderivatives & Indefinite Integrals

Finding antiderivatives. Find all the antiderivatives of the following functions. Check your work by taking derivatives.

g(s) = 1 / (s² + 1)

If F(x) = x² - 3x + C and F (-1) = 4 , what is the value of C?

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

c. F(x) = x² + 10 and G(x) = x² - 100 are antiderivatives of the same function.

29–62. Integrals Evaluate the following integrals. Include absolute values only when needed.

∫ (x²) / (4x³ + 7) dx

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

a. F(x) = x³ - 4x + 100 and G(x) = x³ - 4x - 100 are antiderivatives of the same function.