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Question
Mathematics
If ∫ ( cos θ/5+7 sin θ-2 cos 2 θ) d θ= A log e | B (θ)|+ C where C is a constant of integration, then ( B (θ)/ A ) can be
Q. If
∫
5
+
7
s
i
n
θ
−
2
c
o
s
2
θ
c
o
s
θ
d
θ
=
A
lo
g
e
∣
B
(
θ
)
∣
+
C
where
C
is a constant of integration, then
A
B
(
θ
)
can be
4800
196
JEE Main
JEE Main 2020
Integrals
Report Error
A
5
(
s
i
n
θ
+
3
)
2
s
i
n
θ
+
1
0%
B
s
i
n
θ
+
3
2
s
i
n
θ
+
1
11%
C
2
s
i
n
θ
+
1
5
(
s
i
n
θ
+
3
)
11%
D
s
i
n
θ
+
3
5
(
2
s
i
n
θ
+
1
)
78%
Solution:
∫
5
+
7
s
i
n
θ
−
2
c
o
s
2
θ
c
o
s
θ
d
θ
∫
3
+
7
s
i
n
θ
+
2
s
i
n
2
θ
c
o
s
θ
d
θ
[
s
in
θ
=
t
,
cos
θ
d
θ
=
d
t
]
∫
2
t
2
+
7
t
+
3
d
t
=
∫
(
2
t
+
1
)
(
t
+
3
)
d
t
=
5
1
∫
(
2
t
+
1
2
−
t
+
3
1
)
d
t
=
5
1
ln
∣
∣
t
+
3
2
t
+
1
∣
∣
+
C
=
5
1
ln
∣
∣
s
i
n
θ
+
3
2
s
i
n
θ
+
1
∣
∣
+
C
A
=
5
1
and
B
(
θ
)
=
s
i
n
θ
+
3
2
s
i
n
θ
+
1