Solve the initial value problems in Exercises 55–58.
55. dy/dt = e^t sin(e^t − 2),y(ln 2) = 0

Evaluate the integrals in Exercises 33–54.

∫ (e^(√r) / √r) dr

Evaluate the integrals in Exercises 77–90.

81. ∫dy/(y²-2y+5)

Evaluate the integrals in Exercises 33–54.

∫(from ln3 to ln2) (e^x) dx

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

41. y= x arcsin(x) + √(1-x²)

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

18. y = t√(ln t)

43. Surrounding medium of unknown temperature A pan of warm water (46°C) was put in a refrigerator. Ten minutes later, the water’s temperature was 39°C; 10 min after that, it was 33°C. Use Newton’s Law of Cooling to estimate how cold the refrigerator was.