👉 Try now NerdPal! Our new math app on iOS and Android

# Find the integral $\int\frac{v-1}{v^2}dv$

## Step-by-step Solution

Go!
Math mode
Text mode
Go!
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

###  Solution

$\ln\left(v\right)+\frac{1}{v}+C_0$
Got another answer? Verify it here!

##  Step-by-step Solution 

Problem to solve:

$\int\frac{v-1}{v^2}dv$

Specify the solving method

1

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

$\int\left(\frac{v}{v^2}+\frac{-1}{v^2}\right)dv$

Learn how to solve problems step by step online.

$\int\left(\frac{v}{v^2}+\frac{-1}{v^2}\right)dv$

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

$\ln\left(v\right)+\frac{1}{v}+C_0$

##  Explore different ways to solve this problem

SnapXam A2

Go!
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

###  Join 500k+ students in problem solving.

##### Without automatic renewal.
Create an Account