Simplify $x^3+x^2-14x+\frac{-27}{x}+3$

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 Solution

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Derivative

$\frac{d}{dx}\left(x^3+x^2-14x+\frac{-27}{x}+3\right)=3x^{2}+2x-14+\frac{27}{x^2}$ See full solution 

Integral

$\int\left(x^3+x^2-14x+\frac{-27}{x}+3\right)dx=\frac{x^{4}}{4}+\frac{x^{3}}{3}-7x^2-27\ln\left(x\right)+3x+C_0$ See full solution 

Simplify $x^3+x^2-14x+\frac{-27}{x}+3$