what is the integral of x^2/log(x)

Identify Integral: Identify the integral that needs to be solved. We need to find the integral of the function f(x) = x^2/log(x) with respect to x.Recognize Non-standard Form: Recognize that the integral does not correspond to a standard form and cannot be solved using elementary functions. The integral ∫(x^2/log(x)) dx does not match any basic integration formula or immediate antiderivative, suggesting that it may require a special function or numerical methods for its evaluation.Consider Simplification Techniques: Consider integration techniques that could simplify the problem. Since the integral does not simplify easily, we might consider integration by parts or substitution. However, neither method seems to apply directly here due to the complexity of the denominator log(x).Conclude Special Functions or Numerical Methods: Conclude that the integral likely requires numerical methods or special functions for its evaluation. The integral ∫(x^2/log(x)) dx does not have a closed-form expression in terms of elementary functions. It may be expressed in terms of special functions or evaluated numerically.

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Precalculus

Power property of logarithms

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Q. what is the integral of

\frac{x^2}{\log(x)}

Identify Integral: Identify the integral that needs to be solved. $\newline$ We need to find the integral of the function $f(x) = \frac{x^2}{\log(x)}$ with respect to $x$ .
Recognize Non-standard Form: Recognize that the integral does not correspond to a standard form and cannot be solved using elementary functions. $\newline$ The integral $\int(\frac{x^2}{\log(x)}) \, dx$ does not match any basic integration formula or immediate antiderivative, suggesting that it may require a special function or numerical methods for its evaluation.
Consider Simplification Techniques: Consider integration techniques that could simplify the problem. $\newline$ Since the integral does not simplify easily, we might consider integration by parts or substitution. However, neither method seems to apply directly here due to the complexity of the denominator $\log(x)$ .
Conclude Special Functions or Numerical Methods: Conclude that the integral likely requires numerical methods or special functions for its evaluation. $\newline$ The integral $\int(\frac{x^2}{\log(x)}) dx$ does not have a closed-form expression in terms of elementary functions. It may be expressed in terms of special functions or evaluated numerically.