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# Find the integral $\int\frac{z-1}{5z}dz$

## Step-by-step Solution

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###  Videos

$\frac{1}{5}z-\frac{1}{5}\ln\left(z\right)+C_0$
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##  Step-by-step Solution 

Problem to solve:

$\int\frac{z-1}{5z}dz$

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1

Expand the fraction $\frac{z-1}{5z}$ into $2$ simpler fractions with common denominator $5z$

$\int\left(\frac{z}{5z}+\frac{-1}{5z}\right)dz$

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

$\int\left(\frac{z}{5z}+\frac{-1}{5z}\right)dz$

Learn how to solve integrals of rational functions problems step by step online. Find the integral int((z-1)/(5z))dz. Expand the fraction \frac{z-1}{5z} into 2 simpler fractions with common denominator 5z. Simplify the resulting fractions. Expand the integral \int\left(\frac{1}{5}+\frac{-1}{5z}\right)dz into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{5}dz results in: \frac{1}{5}z.

$\frac{1}{5}z-\frac{1}{5}\ln\left(z\right)+C_0$

##  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

Solve int((z-1)/(5z))dz using partial fractionsSolve int((z-1)/(5z))dz using basic integralsSolve int((z-1)/(5z))dz using u-substitutionSolve int((z-1)/(5z))dz using integration by partsSolve int((z-1)/(5z))dz using trigonometric substitution

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7
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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 Rational Functions

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