integrate the
cosx /e^x
Answers
Answered by
0
Answer:
I don't understand this question dear please snap your question
Answered by
2
Answer:
hey mate this is your answer
Step-by-step explanation:
Integration by parts:
∫
u
d
v
=
u
v
−
∫
v
d
u
let
u
=
cos
(
x
)
, then,
d
v
=
e
x
d
x
,
d
u
=
−
sin
(
x
)
d
x
, and
v
=
e
x
Substitute into the formula:
∫
cos
(
x
)
e
x
d
x
=
cos
(
x
)
e
x
−
∫
−
sin
(
x
)
e
x
d
x
∫
cos
(
x
)
e
x
d
x
=
cos
(
x
)
e
x
+
∫
sin
(
x
)
e
x
d
x
[1]
Integration by parts:
∫
u
d
v
=
u
v
−
∫
v
d
u
let
u
=
sin
(
x
)
,
d
v
=
e
x
d
x
, then,
d
u
=
cos
(
x
)
d
x
, and
v
=
e
x
Substitute into the formula:
∫
sin
(
x
)
e
x
d
x
=
sin
(
x
)
e
x
−
∫
cos
(
x
)
e
x
d
x
Substitute into equation [1]:
∫
cos
(
x
)
e
x
d
x
=
cos
(
x
)
e
x
+
sin
(
x
)
e
x
−
∫
cos
(
x
)
e
x
d
x
Add
∫
cos
(
x
)
e
x
d
x
to both sides:
2
∫
cos
(
x
)
e
x
d
x
=
cos
(
x
)
e
x
+
sin
(
x
)
e
x
Divide by 2:
∫
cos
(
x
)
e
x
d
x
=
1
2
cos
(
x
)
e
x
+
1
2
sin
(
x
)
e
x
Don't forget the constant:
∫
cos
(
x
)
e
x
d
x
=
1
2
cos
(
x
)
e
x
+
1
2
sin
(
x
)
e
x
+
C
mark as brainliest thank you
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