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KEAM 2014 Math Paper
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© examsnet.com
Question : 40
Total: 120
∫
(
1
+
x
)
e
x
s
i
n
2
(
x
e
x
)
dx
is equal to
−
c
o
t
(
e
x
)
+
C
t
a
n
(
x
e
x
)
+
C
t
a
n
(
e
x
)
+
C
c
o
t
(
x
e
x
)
+
C
−
c
o
t
(
x
e
x
)
+
C
Validate
Solution:
Let
I
=
∫
(
1
+
x
)
e
x
sin
2
(
x
e
x
)
d
x
Put
x
e
x
=
t
⇒
(
1
⋅
e
x
+
x
⋅
e
x
)
d
x
=
d
t
⇒
(
1
+
x
)
e
x
d
x
=
d
t
∴
I
=
∫
d
t
sin
2
t
=
∫
c
o
s
e
c
2
t
d
t
=
−
cot
t
+
C
=
−
cot
(
x
e
x
)
+
C
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