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

Step-by-step Solution

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Solution

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Final Answer

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

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Simplify the expression inside the integral

$\int\frac{1-x}{2}dx$

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

$\int\frac{1-x}{2}dx$

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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 expression inside the integral. Take the constant \frac{1}{2} out of the integral. Simplify the expression inside the integral. The integral \frac{1}{2}\int1dx results in: \frac{1}{2}x.

Final Answer

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

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 integral of (x1/2(1+-1x)/x)dx using partial fractionsSolve integral of (x1/2(1+-1x)/x)dx using basic integralsSolve integral of (x1/2(1+-1x)/x)dx using u-substitutionSolve integral of (x1/2(1+-1x)/x)dx using integration by partsSolve integral of (x1/2(1+-1x)/x)dx using trigonometric substitution

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Function Plot

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

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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
D□x
∫
∫◻
|◻|
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

How to improve your answer:

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Main Topic: Integrals of Rational Functions

Integrals of rational functions of the form R(x) = P(x)/Q(x).

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