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Byju's Answer
Standard XII
Mathematics
Functions
∫ e3xcos 4x d...
Question
∫
e
3
x
cos
4
x
d
x
is equal to
( where
C
is the constant of integration)
A
e
3
x
25
(
3
cos
4
x
+
4
sin
4
x
)
+
C
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B
e
2
x
25
(
3
cos
4
x
−
4
sin
4
x
)
+
C
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C
e
3
x
16
(
3
cos
4
x
+
4
sin
4
x
)
+
C
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D
e
3
x
25
(
4
cos
4
x
+
3
sin
4
x
)
+
C
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Solution
The correct option is
A
e
3
x
25
(
3
cos
4
x
+
4
sin
4
x
)
+
C
I
=
∫
e
3
x
cos
4
x
d
x
⇒
I
=
e
3
x
3
2
+
4
2
(
3
cos
4
x
+
4
sin
4
x
)
+
C
(
∵
∫
e
a
x
cos
b
x
=
e
a
x
a
2
+
b
2
(
a
cos
b
x
+
b
sin
b
x
)
)
∴
I
=
e
3
x
25
(
3
cos
4
x
+
4
sin
4
x
)
+
C
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