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Question
Mathematics
The integral ∫(dx/(x+4)8/7(x-3)6/7) is equal to: (where C is a constant of integration)
Q. The integral
∫
(
x
+
4
)
8/7
(
x
−
3
)
6/7
d
x
is equal to :
(where C is a constant of integration)
3556
206
JEE Main
JEE Main 2020
Integrals
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A
−
(
x
+
4
x
−
3
)
−
1/7
+
C
10%
B
2
1
(
x
+
4
x
−
3
)
3/7
+
C
21%
C
(
x
+
4
x
−
3
)
1/7
+
C
58%
D
−
13
1
(
x
+
4
x
−
3
)
−
13/7
+
C
11%
Solution:
I
=
∫
(
x
+
4
)
7
8
(
x
−
3
)
7
6
d
x
=
∫
(
x
−
3
x
+
4
)
7
8
(
x
−
3
)
2
d
x
Let
x
−
3
x
+
4
=
t
⇒
(
x
−
3
)
2
d
x
=
−
7
1
d
t
⇒
I
=
−
7
1
∫
t
8/7
d
t
=
−
7
1
∫
t
−
8/7
d
t
=
t
−
1/7
+
C
=
+
(
x
−
3
x
+
4
)
−
1/7
+
C
=
(
x
+
4
x
−
3
)
1/7
+
C