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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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Final Answer

$\frac{1}{2}x-\frac{1}{4}x^2+C_0$
Got another answer? Verify it here!

Step-by-step Solution

Problem to solve:

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

Specify the solving method

1

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

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

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

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

Unlock the first 2 steps of this solution!

Learn how to solve integrals of rational functions 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.

Final Answer

$\frac{1}{2}x-\frac{1}{4}x^2+C_0$
SnapXam A2
Answer Assistant

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Got another answer? Verify it!

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

Useful tips on how to improve your answer:

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

Used formulas:

4. See formulas

Time to solve it:

~ 0.07 s