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The equation is $\"\\int$ .

The integrand is $\"8x^3+\\frac{1}{2x^2}\"$ .

Consider the right side part $\"f(x)=2x^4-\\frac{1}{2x}+C\"$ .

Apply derivative on each side with respect to $\"x\"$ .

$\"\\frac{d}{dx}f(x)=\\frac{d}{dx}\\left$

Apply power rule of derivatives $\"\\int$ .

$\"=2\\left$

$\"=8x^{3}+\\frac{1}{2}{x^{-2}}\"$

$\"f\'(x)=8x^{3}+\\frac{1}{2x^2}\"$ .

The derivative of right side is equal to the integrand.

$\"\\frac{d}{dx}\\left$ .

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$\"\\frac{d}{dx}\\left$ .