int {frac{{3{x^3} - 2sqrt x }}{x}} dx = | vedclass

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(D) We are given the integral $\int {\frac{{3{x^3} - 2\sqrt x }}{x}} dx$. First,divide each term in the numerator by the denominator $x$: $\int {(\fra

Vedclass · Accepted Answer

$x^3 - 4\sqrt{x} + c$

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(D) We are given the integral $\int {\frac{{3{x^3} - 2\sqrt x }}{x}} dx$. First,divide each term in the numerator by the denominator $x$: $\int {(\frac{{3{x^3}}}{x} - \frac{{2\sqrt x }}{x})} dx = \int {(3{x^2} - 2{x^{1/2 - 1}})} dx$ $= \int {(3{x^2} - 2{x^{ - 1/2}})} dx$. Now,apply the power rule for integration $\int {x^n} dx = \frac{{{x^{n + 1}}}}{{n + 1}} + c$: $= 3 \cdot \frac{{{x^3}}}{3} - 2 \cdot \frac{{{x^{ - 1/2 + 1}}}}{{ - 1/2 + 1}} + c$ $= {x^3} - 2 \cdot \frac{{{x^{1/2}}}}{{1/2}} + c$ $= {x^3} - 4{x^{1/2}} + c$ $= {x^3} - 4\sqrt x + c$.

$\int {\frac{{3{x^3} - 2\sqrt x }}{x}} dx = $

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