Begin2.DVI

Integrals containingX= 2ax−x^2 , a 6 = 0

137. 
     

∫ √

X dx=(x− 2 a)

√

X+a

2

2 sin

− 1

(

x−a

|a|

)

+C

138. 
     

∫ dx

√

X

= sin−^1

(x−a

|a|

)

+C

139. 
     

∫

x

√

X dx= sin−^1

(x−a

|a|

)

+C

140. 
     

∫ x dx

√

X

=−

√

X+asin−^1

(

x−a

|a|

)

+C

141. 
     

∫ dx

X^3 /^2 =

x−a

a^2

√

X

+C

142. 
     

∫ x dx

X^3 /^2 =

x

a

√

X

+C

143. 
     

∫ dx

X =

1

2 aln|

x

x− 2 a|+C

144. 
     

∫ x dx
X =−ln|x−^2 a|+C
145.

∫ dx

X^2 =−

1

4 ax−

1

4 a^2 (x− 2 a)+

1

4 a^2 ln|

x

x− 2 a|+C

146. 
     

∫ x dx

X^2 =−

1

2 a(x− 2 a)+

1

4 a^2 ln|

x

x− 2 a|+C

147. 
     

∫

xn

√

X dx=−n^1 + 2xn−^1 X^3 /^2 +(2nn+ 1)+ 2a

∫

xn−^1

√

X dx, n 6 =− 2

148. 
     

∫ √X dx

xn =

1

(3− 2 n)a

X^3 /^2

xn +

n− 3

(2n−3)a

∫ √X

xn−^1 dx, n^6 = 3/^2

Integrals containingX=ax^2 +bx+cwith ∆ = 4ac−b^2 , ∆ 6 = 0, a 6 = 0

149. 
     

∫ dx

X =















√^1

−∆

ln

( 2 ax+b−√−∆

2 ax+b+

√

−∆

)

+C 1 , ∆< 0

√^2

∆

tan−^12 ax√+b

∆

+C 2 , ∆> 0

−a(x+^1 b/ 2 a)+C 3 , ∆ = 0

150. 
     

∫ x dx

X =

1

2 cln|X| −

b

2 a

∫ 1

Xdx

151. 
     

∫ x (^2) dx
X =
x
a−
b
2 a^2 ln|X|+
2 ac−∆
2 a^2
∫ dx
X
Appendix C