Need help with Calculus Integration with parts

Question

Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for the constant of integration.)

8x² ln x dx;    u = ln x, dv = 8x² dx

Answer 1

u = ln(x) dv = 8x² dx

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differentiate integrate

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V V

du = (1/x) dx v = (8/3)x³

∫ u dv = uv - ∫ v du

Replace the u's and v's as assigned / found above:

∫ 8x² ln(x) dx = ln(x) (8/3)x³ - ∫ (8/3)x³ (1/x) dx

re-write (simplify) the RHS:

= (8/3)x³ ln(x) - ∫ (8/3)x² dx

= (8/3)x³ ln(x) - (8/9)x³

= (8/9)x³ (3•ln(x) - 1) + C