Try now NerdPal! Our new app on iOS and Android

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

## Step-by-step Solution

Go!
Math mode
Text mode
Go!
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

###  Videos

$\frac{1}{2}\left(1-x\right)x+C_0$
Got another answer? Verify it here!

##  Step-by-step Solution 

Problem to solve:

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

Specify the solving method

1

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

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

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$\frac{1}{2}\left(1-x\right)x+C_0$

$\frac{1}{2}\left(1-x\right)x+C_0$

##  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((x1/2(1-x))/x)dx using partial fractionsSolve int((x1/2(1-x))/x)dx using basic integralsSolve int((x1/2(1-x))/x)dx using u-substitutionSolve int((x1/2(1-x))/x)dx using integration by partsSolve int((x1/2(1-x))/x)dx using trigonometric substitution

SnapXam A2

Go!
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

### Main topic:

Differential Calculus

~ 0.02 s

###  Join 500k+ students in problem solving.

##### Without automatic renewal.
Create an Account