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

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##  Final answer to the problem

$-\frac{1}{2}\ln\left|1+v^2\right|+C_0$
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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
Can't find a method? Tell us so we can add it.
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 problems step by step online.

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

Learn how to solve 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.

##  Final answer to the problem

$-\frac{1}{2}\ln\left|1+v^2\right|+C_0$

##  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

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