Integral using Substitution (Complex Exponential Functions)
I =
∫
e
12
x
5
+
105
x
4
-
40
x
3
+
180
x
2
+
120
x
-
15
(
x
4
+
7
x
3
-
2
x
2
+
6
x
+
2
)
d
x
Put
u
=
12
x
5
+
105
x
4
-
40
x
3
+
180
x
2
+
120
x
-
15
, then
d
u
=
(
60
x
4
+
420
x
3
-
120
x
2
+
360
x
+
120
)
d
x
Or,
1
60
d
u
=
(
x
4
+
7
x
3
-
2
x
2
+
6
x
+
2
)
d
x
So,
I =
∫
e
u
(
1
60
)
d
u
Or,
I =
1
60
∫
e
u
d
u
Or,
I =
1
60
e
u
+
C
Or,
I =
1
60
e
12
x
5
+
105
x
4
-
40
x
3
+
180
x
2
+
120
x
-
15
+
C
Algebra
Analytic Geometry
Differential Calculus
Integral Calculus
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Copyright © Dayal D. Purohit, Ph.D.(Mathematics)