Find the integral. $$ \int \left[ \frac{-3}{\sqrt[3]{x}} - 4\sqrt{x} \right] dx $$ A. $$ x^{\frac{2}{3}} - 2x^{\frac{3}{2}} + C $$ B. $$ -3 \ln |x^{\frac{1}{3}}| - 2x^{\frac{3}{2}} + C $$ C. $$ -\frac{9}{2}x^{\frac{2}{3}} - \frac{8}{3}x^{\frac{3}{2}} + C $$ D. $$ -2x^{\frac{2}{3}} - 6x^{\frac{3}{2}} + C $$
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The integral is: $$ \int \left[ \frac{-3}{\sqrt[3]{x}} - 4\sqrt{x} \right] dx $$ First, rewrite the terms using fractional exponents: $$ \sqrt[3]{x} = x^{\frac{1}{3}} $$ $$ \sqrt{x} = x^{\frac{1}{2}} $$ So the expression becomes: $$ \frac{-3}{x^{\frac{1}{3}}} - Show more…
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