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Step-by-step Solution

Integral of $36-\left(6-4x+x^2\right)^2$

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Answer

$24x^2-\frac{1}{5}x^{5}+2x^{4}-\frac{16}{3}x^{3}-4x^{3}+C_0$

Step-by-step explanation

Problem to solve:

$\int_{ }^{ }\left(36-\left(6-4x+x^2\right)^2\right)dx$
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The integral of the sum of two or more functions is equal to the sum of their integrals

$\int36dx+\int-\left(6-4x+x^2\right)^2dx$
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The integral of a constant is equal to the constant times the integral's variable

$36x+\int-\left(6-4x+x^2\right)^2dx$

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Answer

$24x^2-\frac{1}{5}x^{5}+2x^{4}-\frac{16}{3}x^{3}-4x^{3}+C_0$