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

## Step-by-step Solution

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###  Videos

$-\frac{1}{2}\ln\left(x+1\right)-\frac{1}{2}\ln\left(-x+1\right)+C_0$
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##  Step-by-step Solution 

Problem to solve:

$\int\frac{x}{1-x^2}dx$

Specify the solving method

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 integrals by partial fraction expansion problems step by step online.

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

Learn how to solve integrals by partial fraction expansion 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.

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

##  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

Solve int(x/(1-x^2))dx using partial fractionsSolve int(x/(1-x^2))dx using basic integralsSolve int(x/(1-x^2))dx using u-substitutionSolve int(x/(1-x^2))dx using integration by partsSolve int(x/(1-x^2))dx using trigonometric substitution

SnapXam A2

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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

### Main topic:

Integrals by Partial Fraction Expansion

~ 0.1 s

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