integrate: x^2-4/(x^2+1)(x^2+2)(x^2+3) dx
Answers
Answered by
3
Answer:
Explanation:
Our goal should be to make this mirror the arctangent integral:
∫
1
u
2
+
1
d
u
=
arctan
(
u
)
+
C
To get the
1
in the denominator, start by factoring:
∫
1
x
2
+
4
d
x
=
∫
1
4
(
x
2
4
+
1
)
d
x
=
1
4
∫
1
x
2
4
+
1
d
x
Note that we want
u
2
=
x
2
4
, so we let
u
=
x
2
, which implies that
d
u
=
1
2
d
x
.
1
4
∫
1
x
2
4
+
1
d
x
=
1
2
∫
1
2
(
x
2
)
2
+
1
d
x
=
1
2
∫
1
u
2
+
1
d
u
This is the arctangent integral:
1
2
∫
1
u
2
+
1
d
u
=
1
2
arctan
(
u
)
+
C
=
1
2
arctan
(
x
2
)
+
C
Similar questions