Final Answer
$\frac{1}{2}x+\frac{1}{4}x^2+C_0$
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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 $x$
$\int\frac{1}{2}\left(1+x\right)dx$
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$\int\frac{1}{2}\left(1+x\right)dx$
Learn how to solve 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
$\frac{1}{2}x+\frac{1}{4}x^2+C_0$