In Exercises 1–24, find the derivative of y with respect to the appropriate variable.
3. y = (1/4)xe^(4x) - (1/16)e^(4x)

Evaluate the integrals in Exercises 31–78.

31. ∫e^x sin(e^x)dx

133. What is the age of a sample of charcoal in which 90% of the carbon-14 originally present has decayed?

In Exercises 79–84, solve for y.

79. 3^y = 2^(y+1)

Evaluate the integrals in Exercises 31–78.

61. ∫(from 1 to 3)(ln(v+1))²/(v+1) dv

In Exercises 1–24, find the derivative of y with respect to the appropriate variable.

17. y = ln(arccos(x))

Evaluate the integrals in Exercises 31–78.

37. ∫(from -1 to 1)dx/(3x-4)