Final answer to the problem
$\frac{2}{3}a^{3}+4c+\frac{c^{3}}{3}+2a^2-a^2c-2c^2+C_0$
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Step-by-step Solution
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1
Find the integral
$\int\left(a+2-c\right)^2dc$
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$\int\left(a+2-c\right)^2dc$
Learn how to solve problems step by step online. Integrate the function (a+2-c)^2. Find the integral. Rewrite the integrand \left(a+2-c\right)^2 in expanded form. Expand the integral \int\left(a^2+4+c^2+4a-2ac-4c\right)dc into 6 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int a^2dc results in: \frac{a^{3}}{3}.
Final answer to the problem
$\frac{2}{3}a^{3}+4c+\frac{c^{3}}{3}+2a^2-a^2c-2c^2+C_0$