73. Find the area between the curves y=ln(x) and y=ln(2x) from x=1 to x=5.

126. Show that the sum arctan(x)+arctan(1/x) is constant.

Evaluate the integrals in Exercises 91–102.

99. ∫1/(√x (x+1)((arctan√x)²+9)) dx

For problems 49–52 use implicit differentiation to find dy/dx at the given point P.

49. 3arctan(x) + arcsin(y) = π/4; P(1, -1)

Evaluate the integrals in Exercises 41–60.

45. ∫tanh(x/7)dx

128. Derive the formula dy/dx = 1/(1+x²) for the derivative of y = arctan(x) by differentiating both sides of the equivalent equation tan(y)=x.

Evaluate the integrals in Exercises 53–76.

73. ∫(from 0 to ln√3) e^x dx/(1+e^(2x))