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MHT CET 2019 Math Solved Paper
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© examsnet.com
Question : 12
Total: 50
∫
cos
x
+
x
sin
x
x
2
+
x
cos
x
d
x
log
|
x
sin
x
x
+
cos
x
|
+
c
log
|
x
x
+
cos
x
|
+
c
log
|
cos
x
+
x
sin
x
|
+
c
log
|
x
2
+
x
cos
x
|
+
c
Validate
Solution:
Let
I
=
∫
cos
x
+
x
sin
x
x
2
+
x
cos
x
d
x
=
∫
(
x
+
cos
x
)
−
x
(
1
−
sin
x
)
x
(
x
+
cos
)
d
x
.
=
∫
[
1
x
−
(
1
−
sin
x
)
(
x
+
cos
x
)
]
d
x
put
f
(
x
)
=
x
+
cos
x
f
′
(
x
)
=
1
−
sin
x
⇒
I
=
∫
[
1
x
−
f
′
(
x
)
f
(
x
)
]
d
x
=
log
|
x
|
−
log
|
f
(
x
)
|
+
c
=
l
o
g
|
x
x
+
cos
x
|
+
c
© examsnet.com
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