93. S x2 √ɑ + bx dx = 2 (8 a2 – 12 abx + 15 b2x2) √(a + bx)a

105 63

dx
x √ a + bx

n

2

a

b

x

dx

m

(a + bx) 2

n-1dz, ,༧

107. Sf(x, Va+bx)dx="S f ƒ (2* =^, ») da,

b

109. S.ƒ(x, (a + bx)", (a + bx)", · · ·) dx

==

.

where y = a + bx, and s is the least common multiple of n,

2, etc.

B. — EXPRESSIOns Involving BOTH √a + bx AND √a'+b'x.

C. - EXPRESSIONS* INVOLVING √x2±a2 AND √a2 — x2:

† ( x √a2 — x2 + a2 sin−13

· log (x + √x2±a2).

126.

S

a

128. S

dx

dx

a2

129. S

1

log

a

:(a +

a2
dx =

√a2x2

x dx

a2

= ± √a2± x2.

√x2 - a2.

These equations are all special cases of more general equations given in the

next section. For additional formulas consult Equation 66.