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Byju's Answer
Standard XII
Mathematics
Logarithmic Differentiation
∫ fx+gxdx is ...
Question
∫
(
f
(
x
)
+
g
(
x
)
)
d
x
is equal to
A
x
4
4
+
x
2
2
+
x
+
c
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B
x
4
4
+
x
2
3
+
x
2
+
2
x
+
c
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C
x
4
4
+
x
3
3
+
x
2
2
+
x
+
c
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D
x
4
4
+
x
3
3
+
c
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Solution
The correct option is
B
x
4
4
+
x
3
3
+
x
2
2
+
x
+
c
Consider
6
∫
f
(
x
)
g
(
x
)
d
x
=
x
6
+
3
x
4
+
3
x
2
+
c
⇒
∫
f
(
x
)
g
(
x
)
d
x
=
1
6
(
x
6
+
3
x
4
+
3
x
2
+
c
)
Differentiate w.r.t
x
,
⇒
f
(
x
)
g
(
x
)
=
x
5
+
2
x
3
+
x
...........
(
1
)
Consider,
2
∫
g
(
x
)
d
x
f
(
x
)
=
x
2
+
c
⇒
∫
g
(
x
)
d
x
f
(
x
)
=
1
2
(
x
2
+
c
)
Differentiate w.r.t
x
⇒
g
(
x
)
f
(
x
)
=
x
............
(
2
)
(
1
)
×
(
2
)
⇒
(
g
(
x
)
)
2
=
x
6
+
2
x
4
+
x
2
=
(
x
3
+
x
)
2
⇒
g
(
x
)
=
x
3
+
x
(
1
)
(
2
)
⇒
(
f
(
x
)
)
2
=
x
4
+
2
x
2
+
1
=
(
x
2
+
1
)
2
⇒
f
(
x
)
=
x
2
+
1
Then,
∫
(
g
(
x
)
+
f
(
x
)
)
d
x
=
∫
(
x
3
+
x
+
x
2
+
1
)
d
x
=
x
4
4
+
x
3
3
+
x
2
2
+
x
+
c
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0
Similar questions
Q.
∫
(
x
+
x
2
+
x
3
+
x
4
)
dx is equal to
Q.
The solution of the differential equation
x
d
y
d
x
+
y
=
x
2
+
3
x
+
2
is