Final Answer
$\frac{x^{3}}{6}+\frac{1}{2}x^2+C_0$
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Step-by-step Solution
Problem to solve:
$\int\left(\frac{1}{2}x^2+x\right)dx$
Specify the solving method
1
Expand the integral $\int\left(\frac{1}{2}x^2+x\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
$\int\frac{1}{2}x^2dx+\int xdx$
Learn how to solve integrals of polynomial functions problems step by step online.
$\int\frac{1}{2}x^2dx+\int xdx$
Learn how to solve integrals of polynomial functions problems step by step online. Integrate int(1/2x^2+x)dx. Expand the integral \int\left(\frac{1}{2}x^2+x\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{2}x^2dx results in: \frac{x^{3}}{6}. The integral \int xdx results in: \frac{1}{2}x^2. Gather the results of all integrals.
Final Answer
$\frac{x^{3}}{6}+\frac{1}{2}x^2+C_0$