Evaluate the integrals in Exercises 39–56.
49. ∫3sec²t/(6 + 3tan(t)) dt

Evaluate the integrals in Exercises 41–60.

51. ∫(from ln2 to ln4)coth(x)dx

Evaluate the integrals in Exercises 39–56.

45. ∫(from 1 to 2)(2ln x)/x dx

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.

In Exercises 73 and 74, repeat the steps above to solve for the functions y=f(x) and x=f^(-1)(y) defined implicitly by the given equations over the interval.

73. y^(1/3) - 1 = (x+2)³, -5 ≤ x ≤ 5, x_0 = -3/2

Verify the integration formulas in Exercises 111–114.

111. ∫ (arctan x) / x² dx = ln x - 1/2 ln(1 + x²) - arctan x / x + C