11. Integrals of Inverse, Exponential, & Logarithmic Functions

Evaluate the integrals in Exercises 31–78.

71. ∫(from √2/3 to 2/3)dy/(|y|√(9y²-1))

Evaluate the integrals in Exercises 31–78.

73. ∫dx/√(-2x-x²)

Evaluate the integrals in Exercises 67–74 in terms of

a. inverse hyperbolic functions.

71. ∫(from 1/5 to 3/13)dx/(x√(1-16x²))

Evaluate the integrals in Exercises 67–74 in terms of

a. inverse hyperbolic functions.

73. ∫(from 0 to π)cos(x)dx/√(1+sin²x)

Evaluate the integrals in Exercises 31–78.

75. ∫(from -2 to -1)2dv/(v²+4v+5)

Evaluate the integrals in Exercises 31–78.

77. ∫dt/((t+1)√(t²+2t-8))

Evaluate the integrals in Exercises 77–90.

81. ∫dy/(y²-2y+5)

Evaluate the integrals in Exercises 77–90.

84. ∫(from 2 to 4)2dx/(x²-6x+10)

Evaluate the integrals in Exercises 77–90.

90. ∫dx/((x-2)√(x²-4x+3))

Evaluate the integrals in Exercises 91–102.

96. ∫dy/((arcsin y)(1-y²))

Evaluate the integrals in Exercises 91–102.

102. ∫(from -1/3 to 1/√3)(cos(arctan 3x))/(1+9x²) dx

Evaluate the integrals in Exercises 91–102.

93. ∫(arcsin x)²dx/√(1-x²)

Evaluate the integrals in Exercises 91–102.

99. ∫1/(√x (x+1)((arctan√x)²+9)) dx

Verify the integration formulas in Exercises 37–40.

37. a. ∫sech(x)dx = tan⁻¹(sinh x) + C

Verify the integration formulas in Exercises 37–40.

37. b. ∫sech(x)dx = sin⁻¹(tanh x) + C