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Algebra Baldor
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Find the integral $\int e^{-x}\cos\left(2x\right)dx$

Used Formulas

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Solution

Formulas

Videos

Derivatives of trigonometric functions

· Derivative of the cosine function
$\frac{d}{dx}\left(\cos\left(\theta \right)\right)=-\frac{d}{dx}\left(\theta \right)\sin\left(\theta \right)$
· Derivative of the sine function
$\frac{d}{dx}\left(\sin\left(\theta \right)\right)=\frac{d}{dx}\left(\theta \right)\cos\left(\theta \right)$

Basic Derivatives

· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$

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

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

Function Plot

Plotting: $-\frac{1}{5}e^{-x}\cos\left(2x\right)+\frac{2}{5}e^{-x}\sin\left(2x\right)+C_0$

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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

How to improve your answer:

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Find the integral

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

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 (7)

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