Evaluate the integrals in Exercises 41–60.
45. ∫tanh(x/7)dx

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 39–56.

45. ∫(from 1 to 2)(2ln x)/x dx

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

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 39–56.

49. ∫3sec²t/(6 + 3tan(t)) dt