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Find the integral $\int e^{3a}\cos\left(3a\right)da$

Used Formulas

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Solution

Formulas

Videos

Integration Techniques

· Integration by Substitution
$\int f\left(x\right)dx=\int f\left(g\left(t\right)\right) g'\left(t\right)dt$
· Integration by Parts
$\int udv=uv - \int vdu$

Basic Integrals

$\int e^xdx=e^x+C$
· Constant factor Rule
$\int cxdx=c\int xdx$

Function Plot

Plotting: $\frac{1}{6}e^{3a}\cos\left(3a\right)+\frac{1}{6}e^{3a}\sin\left(3a\right)+C_0$

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1
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4
5
6
7
8
9
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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$\int e^xcos2xdx$

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$\int e^x\cdot\cos\left(x\right)dx$

Find the integral

$\int e^{2x}cos\:x\:dx$

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 (4)

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