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# Find the integral $\int\frac{x^{\left(2-1\right)}}{x^2+1}dx$

## Step-by-step Solution

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###  Videos

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

Specify the solving method

We could not solve this problem by using the method: Integrate by partial fractions

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Subtract the values $2$ and $-1$

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

Learn how to solve differential calculus problems step by step online.

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

Learn how to solve differential calculus problems step by step online. Find the integral int((x^(2-1))/(x^2+1))dx. Subtract the values 2 and -1. We can solve the integral \int\frac{x}{x^2+1}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that x^2+1 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dx in the previous equation.

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

##  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 integral of ((x^(2-1))/(x^2+1))dx using basic integralsSolve integral of ((x^(2-1))/(x^2+1))dx using u-substitutionSolve integral of ((x^(2-1))/(x^2+1))dx using integration by partsSolve integral of ((x^(2-1))/(x^2+1))dx using trigonometric substitution

SnapXam A2

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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

### Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.