**Reference: Thomas’s Calculus: 12th edition.**

**Basic Forms:**

- where k is any number
- where
- where
- where
- where

**Forms involving ax+b:**

21. , where

22. , where .

23.

24.

25.

26.

27. , where

28.

29a.

$$$29b.

30.

31.

**Forms involving **

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

**Forms involving **

42.

43.

44.

45.

46.

47.

48.

49.

50.

51.

**Forms involving **

52.

53.

54. , where

55., where

56. , where

57.

58.

59.

60.

61.

62.

**Trigonometric Forms**

63.

64.

65.

66.

67.

68.

69A. , where

69B. , where

69C. , where

70.

71. , where

72.

73. , where

74.

75. , where , (reduces )

76. , where , (reduces )

77. , where

78/ , where

79.

80.

81. , where

82. , where

83.

84.

85.

86.

87.

88.

89.

90. .

91.

92.

93. , where

94. , where

95.

96.

97.

98.

99. , where

100. , where

101. , where

102. , where

**Inverse Trigonometric Forms:**

103.

104.

105.

106. , where

107. , where

108. , where

**Exponential and Logarithmic Forms**

109.

110. , where

111.

112.

113. , where

114.

115.

116.

117. , where

118. , where

119.

**Forms involving **, where

120.

121.

122.

123.

124.

125.

126.

127.

128.

**Hyperbolic Forms**

129.

130.

131.

132.

133. , where

134. , where

135.

136.

137.

138.

139.

140.

141.

142.

143. , where

144. , where

145.

146.

147.

148.

149. , where

150. , where

151. , where

152. , where

153. , where

154. , where

**Some definite integrals**

155. , where

156. , where

157A. when n is an even integer greater than or equal to 2

157B. , if n is an odd integer greater than or equal to 3