Evaluate the integrals in Exercises 53–76.
75. ∫y dy/√(1-y^4)

Evaluate the integrals in Exercises 77–90.

79. ∫(from -1 to 0)6dt/√(3-2t-t²)

Solve the initial value problems in Exercises 115–120.

117. dy/dx = 1/(x√(x² - 1)), x > 1; y(2) = π

Solve the differential equation in Exercises 9–22.

10. (dy/dx) = x²√y, y > 0

Evaluate the integrals in Exercises 91–102.

96. ∫dy/((arcsin y)(1-y²))

Each of Exercises 25–36 gives a formula for a function y=f(x). In each case, find f^(-1)(x) and identify the domain and range of f^(-1). As a check, show that f(f^(-1)(x))=f^(-1)(f(x))=x.

f(x) = x⁵

Finding Antiderivatives

In Exercises 1–16, find an antiderivative for each function. Do as many as you can mentally. Check your answers by differentiation.

(-3/2)csc²x(3x/2)