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Manipal Entrance Test 2018 Math Paper
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© examsnet.com
Question : 50
Total: 70
∫
2
d
x
(
e
x
+
e
−
x
)
2
is equal to
−
e
−
x
(
e
x
+
e
−
x
)
+
c
−
1
(
e
x
+
e
−
x
)
+
c
1
(
e
x
+
1
)
2
+
c
1
(
e
x
−
e
−
x
)
2
+
c
Validate
Solution:
Let
I
=
∫
2
d
x
(
e
x
+
e
−
x
)
2
=
∫
2
d
x
e
2
x
+
e
−
2
x
+
2
=
∫
2
e
2
x
d
x
e
4
x
+
2
e
2
x
+
1
Put
e
2
x
=
t
⇒
2
e
2
x
d
x
=
d
t
∴
I
=
∫
d
t
t
2
+
2
t
+
1
=
∫
d
t
(
t
+
1
)
2
=
−
1
t
+
1
+
c
=
−
1
e
2
x
+
1
=
−
e
−
x
e
x
+
e
−
x
+
c
© examsnet.com
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