3x+1
Evaluate
dx
2x^2 - x+5
Answers
Answered by
1
ANSWER
I=∫
2x
2
+x+1
3x+1
dx
=
4
3
∫
2x
2
+x+1
4x+1
dx+
4
1
∫
2x
2
+x+1
dx
Substitute 2x
2
+x+1=t for first
∴(4x+1)dx=dt
∴I=
4
3
∫
t
dt
+
8
1
∫
x
2
+
2
1
x+
2
1
dx
=
4
3
logt+
8
1
∫
(x+
4
1
)
2
+
2
1
−
16
1
dx
=
4
3
log(2x
2
+x+1)+
8
1
∫
(x+
2
1
)
2
+(
4
7
)
2
dx
=
4
3
log(2x
2
+x+1)+
8
1
.
(7)
/4
1
tan
−1
(7)
/4
x+
4
1
+C
=
4
3
log(2x
2
+x+1)+
2
(7)
1
tan
−1
(7)
4x+1
+C
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