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# Find the integral $\int\frac{\arctan\left(x\right)}{x}dx$

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##  Final answer to the problem

$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(2n+1\right)}}{\left(2n+1\right)^2}+C_0$
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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

Rewrite the function $\arctan\left(x\right)$ as it's representation in Maclaurin series expansion

$\int\frac{\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^n}{2n+1}x^{\left(2n+1\right)}}{x}dx$

Learn how to solve problems step by step online.

$\int\frac{\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^n}{2n+1}x^{\left(2n+1\right)}}{x}dx$

Learn how to solve problems step by step online. Find the integral int(arctan(x)/x)dx. Rewrite the function \arctan\left(x\right) as it's representation in Maclaurin series expansion. Bring the denominator x inside the power serie. Simplify the expression. We can rewrite the power series as the following.

##  Final answer to the problem

$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(2n+1\right)}}{\left(2n+1\right)^2}+C_0$

##  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