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

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Final answer to the problem

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

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Apply the formula: $\sin\left(\theta \right)$$=\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^n}{\left(2n+1\right)!}\theta ^{\left(2n+1\right)}$

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

Learn how to solve calcul intégral problems step by step online.

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

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Learn how to solve calcul intégral problems step by step online. Find the integral int(sin(x)/x)dx. Apply the formula: \sin\left(\theta \right)=\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^n}{\left(2n+1\right)!}\theta ^{\left(2n+1\right)}. Apply the formula: \frac{\sum_{a}^{b} x}{y}=\sum_{a}^{b} \frac{x}{y}, where a=n=0, b=\infty , x=\frac{{\left(-1\right)}^n}{\left(2n+1\right)!}x^{\left(2n+1\right)} and y=x. Simplify the expression. Apply the formula: \int\sum_{a}^{b} \frac{x}{c}dx=\sum_{a}^{b} \frac{1}{c}\int xdx, where a=n=0, b=\infty , c=\left(2n+1\right)! and x={\left(-1\right)}^nx^{2n}.

Final answer to the problem

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

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Function Plot

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

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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

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