Integral using Substitution (Polynomials and Rationals)
I =
∫
6
x
2
-
9
x
+
9
(
12
x
3
-
27
x
2
+
54
x
-
2
)
3
d
x
Put
u
=
12
x
3
-
27
x
2
+
54
x
-
2
, then
d
u
=
(
36
x
2
-
54
x
+
54
)
d
x
or,
(
1
6
)
d
u
=
(
6
x
2
-
9
x
+
9
)
d
x
I =
∫
(
u
)
-3
(
1
6
)
d
u
I =
1
6
∫
(
u
)
-3
d
u
I =
1
6
(
u
)
-2
-2
+
C
I =
1
6
-1
2
(
u
)
2
+
C
I =
-1
12
(
12
x
3
-
27
x
2
+
54
x
-
2
)
2
+
C
Algebra
Analytic Geometry
Differential Calculus
Integral Calculus
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Copyright © Dayal D. Purohit, Ph.D.(Mathematics)