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