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

## Step-by-step Solution

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$\frac{x^{3}}{6}+\frac{1}{2}x^2+C_0$
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##  Step-by-step Solution 

Problem to solve:

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

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1

Expand the integral $\int\left(\frac{1}{2}x^2+x\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int\frac{1}{2}x^2dx+\int xdx$

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

$\int\frac{1}{2}x^2dx+\int xdx$

Learn how to solve integrals of polynomial functions problems step by step online. Integrate int(1/2x^2+x)dx. Expand the integral \int\left(\frac{1}{2}x^2+x\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{2}x^2dx results in: \frac{x^{3}}{6}. The integral \int xdx results in: \frac{1}{2}x^2. Gather the results of all integrals.

$\frac{x^{3}}{6}+\frac{1}{2}x^2+C_0$

##  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

Solve int(1/2x^2+x)dx using partial fractionsSolve int(1/2x^2+x)dx using basic integralsSolve int(1/2x^2+x)dx using u-substitutionSolve int(1/2x^2+x)dx using integration by partsSolve int(1/2x^2+x)dx using trigonometric substitution

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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 Polynomial Functions

~ 0.05 s

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