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General Integration of math expressions Select all expressions matching the value of indefinite integral int (3x^2-(3)/(x))dx x^3-3lnx x^3-(3)/(x^2)+C x^3-3lnx+C

Вопрос

General Integration of math expressions
Select all expressions matching the value of indefinite integral
int (3x^2-(3)/(x))dx
x^3-3lnx
x^3-(3)/(x^2)+C
x^3-3lnx+C

General Integration of math expressions Select all expressions matching the value of indefinite integral int (3x^2-(3)/(x))dx x^3-3lnx x^3-(3)/(x^2)+C x^3-3lnx+C

Решения

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элита · Репетитор 8 лет

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The correct answer is:<br /><br />$x^{3}-3lnx+C$<br /><br />Explanation: The indefinite integral of the given expression $\int (3x^{2}-\frac {3}{x})dx$ can be evaluated by integrating each term separately. The integral of $3x^{2}$ is $x^{3}$, and the integral of $-\frac{3}{x}$ is $-3lnx$. Therefore, the correct expression matching the value of the indefinite integral is $x^{3}-3lnx+C$, where $C$ represents the constant of integration.
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