(39)
Z
1
√
ax
2
+ bx + c
dx =
1
√
a
ln
2ax + b +2
p
a(ax
2
+ bx + c)
(40)
Z
x
√
ax
2
+ bx + c
dx =
1
a
√
ax
2
+ bx + c-
b
2a
3/2
ln
2ax + b +2
p
a(ax
2
+ bx + c)
(41)
Z
dx
(a
2
+ x
2
)
3/2
=
x
a
2
√
a
2
+ x
2
Integrals with Logarithms
(42)
Z
ln ax dx = x ln ax - x
(43)
Z
x ln x dx =
1
2
x
2
ln x -
x
2
4
(44)
Z
x
2
ln x dx =
1
3
x
3
ln x -
x
3
9
(45)
Z
x
n
ln x dx = x
n+1
ln x
n +1
-
1
(n + 1)
2
, n 6= -1
(46)
Z
ln ax
x
dx =
1
2
(ln ax)
2
(47)
Z
ln x
x
2
dx = -
1
x
-
ln x
x
5
