Identify the correct form of ∫x^2 ln(x) dx using integration by parts.

Question

Edzy · Accepted Answer

Using u = ln(x), dv = x^2 dx gives du = (1/x)dx and v = (1/3)x^3. Thus, ∫x^2 ln(x) dx = x^2 ln(x) - 2∫(1/3)x^3(1/x)dx = x^2 ln(x) - (2/3)∫x^2 dx. The others do not represent the proper applications.

Identify the correct form of ∫x^2 ln(x) dx using integration by parts.

Identify the correct form of ∫x^2 ln(x) dx using integration by parts.

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