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

## Step-by-step Solution

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###  Solution

$\frac{1}{2}x+\frac{1}{4}x^2+C_0$
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##  Step-by-step Solution 

Problem to solve:

$\int\frac{\frac{1}{2}x\left(1+x\right)}{x}dx$

Specify the solving method

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Simplify the fraction $\frac{\frac{1}{2}x\left(1+x\right)}{x}$ by $x$

$\int\frac{1}{2}\left(1+x\right)dx$

Learn how to solve problems step by step online.

$\int\frac{1}{2}\left(1+x\right)dx$

Learn how to solve problems step by step online. Find the integral int((x1/2(1+x))/x)dx. Simplify the fraction \frac{\frac{1}{2}x\left(1+x\right)}{x} by x. The integral of a function times a constant (\frac{1}{2}) is equal to the constant times the integral of the function. Expand the integral \int\left(1+x\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \frac{1}{2}\int1dx results in: \frac{1}{2}x.

$\frac{1}{2}x+\frac{1}{4}x^2+C_0$

##  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

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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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