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

Step-by-step Solution

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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

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  • 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
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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 integral calculus problems step by step online.

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

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Learn how to solve integral calculus 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 inside the integral. We can rewrite the power series as the following.

Final answer to the problem

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

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Function Plot

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

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1
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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

How to improve your answer:

Main Topic: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

Used Formulas

See formulas (2)

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