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# Find the integral $\int\left(x^{-1}+e^{-21x}\right)dx$

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asin
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##  Final answer to the problem

$\ln\left|x\right|+\frac{1}{-21}e^{-21x}+C_0$
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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
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Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$\int\left(\frac{1}{x}+e^{-21x}\right)dx$

Learn how to solve integrals of exponential functions problems step by step online.

$\int\left(\frac{1}{x}+e^{-21x}\right)dx$

Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(x^(-1)+e^(-21x))dx. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Expand the integral \int\left(\frac{1}{x}+e^{-21x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{x}dx results in: \ln\left|x\right|. The integral \int e^{-21x}dx results in: \frac{1}{-21}e^{-21x}.

##  Final answer to the problem

$\ln\left|x\right|+\frac{1}{-21}e^{-21x}+C_0$

##  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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1
2
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: 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.