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Byju's Answer
Standard XII
Mathematics
Binomial Coefficients
Evaluate ∫x7 ...
Question
Evaluate
∫
x
7
d
x
(
1
−
x
2
)
5
(where
C
is constant of integration)
A
−
x
8
8
(
1
−
x
2
)
4
+
C
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B
x
8
8
(
1
−
x
2
)
4
+
C
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C
x
4
8
(
1
−
x
2
)
4
+
C
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D
−
x
4
8
(
1
−
x
2
)
4
+
C
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Solution
The correct option is
B
x
8
8
(
1
−
x
2
)
4
+
C
Let
I
=
∫
x
7
d
x
(
1
−
x
2
)
5
=
∫
x
7
d
x
x
10
(
x
−
2
−
1
)
5
⇒
I
=
∫
x
−
3
d
x
(
x
−
2
−
1
)
5
Put :
x
−
2
−
1
=
t
⇒
−
2
x
−
3
d
x
=
d
t
⇒
I
=
−
1
2
∫
d
t
t
5
⇒
I
=
−
1
2
∫
t
−
5
d
t
=
1
2
⋅
t
−
4
4
+
C
⇒
I
=
1
8
1
(
x
−
2
−
1
)
4
+
C
∴
I
=
x
8
8
(
1
−
x
2
)
4
+
C
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Standard XII Mathematics
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