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Find the integral $\int e^{-x}\cos\left(3x\right)dx$

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Solution

Formulas

Videos

_-substitution: definite integral of exponential function | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=1ct7LUx23io

integral of arcsin x

https://www.youtube.com/watch?v=qwHhwdvTGdY

2011 Calculus AB Free Response #1 parts b c d | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=OSipkz8vDjE

Integral of e^sqrt(x)

https://www.youtube.com/watch?v=9XBL54j-3Eg

2011 Calculus AB Free Response #1 parts b c d | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=QackTJWqOjA

Integrating Exponential Functions, Antiderivatives, Integration By Substitution, Calculus

https://www.youtube.com/watch?v=D9dqdbCgJQM

Function Plot

Plotting: $-\frac{1}{10}e^{-x}\cos\left(3x\right)+\frac{3}{10}e^{-x}\sin\left(3x\right)+C_0$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Integrals of Exponential Functions

Those are integrals that involve exponential functions. Recall that an exponential function is a function of the form f(x)=a^x.

Used Formulas

See formulas (7)

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