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# Solve the integral of logarithmic functions $\int\frac{3^x}{\ln\left(3\right)}dx$

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asin
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sinh
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asinh
acosh
atanh
acoth
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##  Final answer to the problem

$\frac{3^x}{\ln\left|3\right|^2}+C_0$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
Can't find a method? Tell us so we can add it.
1

Take the constant $\frac{1}{\ln\left|3\right|}$ out of the integral

$\frac{1}{\ln\left|3\right|}\int3^xdx$

Learn how to solve integral calculus problems step by step online.

$\frac{1}{\ln\left|3\right|}\int3^xdx$

Learn how to solve integral calculus problems step by step online. Solve the integral of logarithmic functions int((3^x)/ln(3))dx. Take the constant \frac{1}{\ln\left|3\right|} out of the integral. The integral of the exponential function is given by the following formula \displaystyle \int a^xdx=\frac{a^x}{\ln(a)}, where a > 0 and a \neq 1. Simplify the expression. As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration C.

##  Final answer to the problem

$\frac{3^x}{\ln\left|3\right|^2}+C_0$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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3
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
Dx
|◻|
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

###  Main Topic: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.