Evaluate the integrals in Exercises 97–110.
99. ∫₀³ (√2 + 1)x^(√2) dx

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) = 1/x², x > 0

Verify the integration formulas in Exercises 111–114.

113. ∫ (arcsin x)² dx = x(arcsin x)² - 2x + 2 √(1 - x²) arcsin x + C

In Exercises 13–24, find the derivative of y with respect to the appropriate variable.

17. y = ln(sinh z)

Find the values in Exercises 9–12.

9. sin(arccos((√2)/2))

86. Use a derivative to show that g(x)=√(x² + ln x) is one-to-one.

Rewrite the expressions in Exercises 5–10 in terms of exponentials and simplify the results as much as you can.

6. sinh(2ln x)