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Find the integral $\int\frac{5-e^x}{e^{2x}}dx$

Used Formulas

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Solution

Formulas

Videos

Integration Techniques

· Integration by Substitution
$\int f\left(x\right)dx=\int f\left(g\left(t\right)\right) g'\left(t\right)dt$

Basic Integrals

· Sum Rule for Integration
$\int\left(a+b+...\right)dx=\int adx+\int bdx+...$
· Constant factor Rule
$\int cxdx=c\int xdx$
· Power Rule of Integration
$\int x^ndx=\frac{x^{\left(n+1\right)}}{n+1}+C$

Function Plot

Plotting: $-\frac{5}{2}e^{-2x}+\frac{1}{e^x}+C_0$

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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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Similar Problems Solved

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$\int\left(x^2-2x+1\right)e^{2x}dx$

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$\int\frac{1}{1+e^{-2x}}dx$

Find the integral

$\int x^2e^{2x+1}dx$

Find the integral

$\int x\left(x^2-3\right)dx$

Find the integral

$\int x^2e^xdx$

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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