Evaluate the integrals in Exercises 33–54.
51. ∫ from ln(π/6) to ln(π/2) 2e^v cos(e^v) dv

In Exercises 25–36, find the derivative of y with respect to the appropriate variable.

25. y = sinh⁻¹(√x)

Evaluate the integrals in Exercises 111–114.

112. ∫₁^(eˣ) (1 / t) dt

Evaluate the integrals in Exercises 91–102.

93. ∫(arcsin x)²dx/√(1-x²)

In Exercises 57–70, use logarithmic differentiation to find the derivative of y with respect to the given independent variable.

59. y = √(t/(t+1))

Evaluate the integrals in Exercises 77–90.

90. ∫dx/((x-2)√(x²-4x+3))

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

15. y = 2√t tanh(√t)