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

## Step-by-step Solution

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$\ln\left(x\right)-\frac{1}{21}e^{-21x}+C_0$
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##  Step-by-step Solution 

Problem to solve:

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

Specify the solving method

1

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

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

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

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

Learn how to solve integral calculus 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. Simplify the expression inside the integral. 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}.

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

##  Explore different ways to solve this problem

SnapXam A2

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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
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

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