# Step-by-step Solution

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
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

## Step-by-step explanation

Problem to solve:

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

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

$x=\sin\left(\theta \right)$

Learn how to solve integrals of rational functions problems step by step online. Integral of x/(1-x^2) with respect to x. We can solve the integral \int\frac{x}{1-x^2}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above. Substituting in the original integral, we get. Applying the trigonometric identity: 1-\sin\left(\theta\right)^2=\cos\left(\theta\right)^2.

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

### Problem Analysis

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

### Main topic:

Integrals of Rational Functions

~ 0.05 seconds