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# Find the integral $\int\frac{x}{x^2+y^2}dx$

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##  Final answer to the problem

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

We can solve the integral $\int\frac{x}{x^2+y^2}dx$ by applying integration method of trigonometric substitution using the substitution

$x=y\tan\left(\theta \right)$

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

$x=y\tan\left(\theta \right)$

Learn how to solve integrals of rational functions problems step by step online. Find the integral int(x/(x^2+y^2))dx. We can solve the integral \int\frac{x}{x^2+y^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. Factor the polynomial y^2\tan\left(\theta \right)^2+y^2 by it's greatest common factor (GCF): y^2.

##  Final answer to the problem

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

##  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

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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: Integrals of Rational Functions

Integrals of rational functions of the form R(x) = P(x)/Q(x).

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