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Simplify $-3x^5+2x^3-3x+\frac{2}{x^2}+1$

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Derivative

$\frac{d}{dx}\left(-3x^5+2x^3-3x+\frac{2}{x^2}+1\right)=-15x^{4}+6x^{2}-3+\frac{-4x}{x^{4}}$ See full solution

Integral

$\int\left(-3x^5+2x^3-3x+\frac{2}{x^2}+1\right)dx=-\frac{1}{2}x^{6}+\frac{1}{2}x^{4}-\frac{3}{2}x^2+\frac{-2}{x}+x+C_0$ See full solution

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SimplifyWrite in simplest formFactorFactor by completing the squareFind the integralFind the derivativeFind -3x^5+2x^3 using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

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Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

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