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The integral of x^3*ln(x) is (x^4/4)*(ln(x)-1/4).

To solve this integral, we can use integration by parts. Let u = ln(x) and dv = x^3 dx. Then du = 1/x dx and v = x^4/4. Using the formula for integration by parts, we have:

∫x^3 ln(x) dx = uv - ∫v du

= (x^4/4) ln(x) - ∫(x^4/4) (1/x) dx

= (x^4/4) ln(x) - ∫x^3 dx

= (x^4/4) ln(x) - (x^4/16) + C

= (x^4/4) (ln(x) - 1/4) + C

Therefore, the integral of x^3*ln(x) is (x^4/4)*(ln(x)-1/4) + C, where C is the constant of integration.

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