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Find the integral $\int5^x\cdot x^2dx$

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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

How to find the integral of an exponential function using u sub

https://www.youtube.com/watch?v=Sp6tUzUoSps

Calculus - Find the derivative of natural logarithm using product property, d(ln(2x))/dx

https://www.youtube.com/watch?v=urYZhqwUTI0

Derivatives of Exponential Functions

https://www.youtube.com/watch?v=yg_497u6JnA

Definite integral of rational function | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=4WJUEXIksH0

Derivative of x^x^x, Logarithmic Differentiation of Exponential Functions, Calculus Youtube Video

https://www.youtube.com/watch?v=Vhltl9w6QNM

Function Plot

Plotting: $\frac{5^x\cdot x^2}{\ln\left(5\right)}+\frac{-2\cdot 5^x\cdot x}{\ln\left(5\right)^2}+\frac{2\cdot 5^x}{\ln\left(5\right)^{3}}+C_0$

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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 (1)

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