ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# Find the integral $\int\frac{x}{1-x^2}dx$

Go!
Symbolic 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

##  Final answer to the problem

$-\frac{1}{2}\ln\left|x+1\right|-\frac{1}{2}\ln\left|-x+1\right|+C_0$
Got another answer? Verify it here!

##  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 $\frac{x}{1-x^2}$ inside the integral in factored form

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

Learn how to solve problems step by step online.

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

Learn how to solve problems step by step online. Find the integral int(x/(1-x^2))dx. Rewrite the expression \frac{x}{1-x^2} inside the integral in factored form. Rewrite the fraction \frac{x}{\left(1+x\right)\left(1-x\right)} in 2 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B. The first step is to multiply both sides of the equation from the previous step by \left(1+x\right)\left(1-x\right). Multiplying polynomials.

##  Final answer to the problem

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

##  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