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Byju's Answer
Standard XII
Mathematics
Special Integrals - 1
∫ex1+x/sin2xe...
Question
∫
e
x
(
1
+
x
)
s
i
n
2
(
x
e
x
)
d
x
=
A
tan
(
x
e
x
)
+
c
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B
−
cot
(
x
e
x
)
+
c
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C
sin
(
x
e
x
)
+
c
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D
sin
e
x
+
c
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Solution
The correct option is
B
−
cot
(
x
e
x
)
+
c
l
e
t
x
e
x
=
t
(
e
x
+
x
e
x
)
d
x
=
d
t
e
x
(
1
+
x
)
d
x
=
d
t
∫
d
t
s
i
n
2
t
=
∫
c
o
s
e
c
2
t
d
t
=
−
c
o
t
t
+
c
=
−
c
o
t
(
x
e
x
)
+
c
∫
e
x
(
1
+
x
)
s
i
n
2
(
x
e
x
)
d
x
=
−
c
o
t
(
x
e
x
)
+
c
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Similar questions
Q.
equals
A. − cot (
ex
x
) + C
B. tan (
xe
x
) + C
C. tan (
e
x
) + C
D. cot (
e
x
) + C