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

## Step-by-step Solution

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### Videos

$-\ln\left(\sqrt{1+v^2}\right)+C_0$
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## Step-by-step Solution

Problem to solve:

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

Specify the solving method

1

Rewrite the expression $\frac{v}{-1-v^2}$ inside the integral in factored form

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

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

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

Learn how to solve integrals of rational functions problems step by step online. Find the integral int(v/(-1-v^2))dv. Rewrite the expression \frac{v}{-1-v^2} inside the integral in factored form. Take the constant \frac{1}{-1} out of the integral. We can solve the integral -\int\frac{v}{1+v^2}dv by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dv, we need to find the derivative of v. We need to calculate dv, we can do that by deriving the equation above.

$-\ln\left(\sqrt{1+v^2}\right)+C_0$
SnapXam A2

### beta Got another answer? Verify it!

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

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

### Main topic:

Integrals of Rational Functions

~ 0.05 s