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Byju's Answer
Standard XII
Mathematics
Differentiation of a Determinant
If ∫12x2+x-1d...
Question
If
∫
1
2
x
2
+
x
−
1
d
x
=
1
k
ln
∣
∣
∣
2
x
−
1
2
x
+
2
∣
∣
∣
+
C
, then the value of
k
2
+
1
is
(where
C
is integration constant)
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Solution
I
=
∫
1
2
x
2
+
x
−
1
d
x
=
1
2
∫
d
x
x
2
+
x
2
−
1
2
=
1
2
∫
d
x
(
x
+
1
4
)
2
−
(
3
4
)
2
=
1
2
×
1
2
⋅
3
4
ln
∣
∣ ∣ ∣ ∣
∣
x
+
1
4
−
3
4
x
+
1
4
+
3
4
∣
∣ ∣ ∣ ∣
∣
+
C
=
1
3
ln
∣
∣
∣
2
x
−
1
2
x
+
2
∣
∣
∣
+
C
⇒
k
=
3
∴
k
2
+
1
=
10
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Similar questions
Q.
If
∫
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−
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d
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=
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, where
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Differentiation of a Determinant
Standard XII Mathematics
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