Question

Solve dy/dx = log (x*(x^2))

Answer 1

You might want to clarify the question.  Do you mean 'solve for y' or something else?

dy/dx = log( x*(x^2))

dy/dx = log(x^3)

dy/dx = 3log(x)

dy = 3log(x)dx

y = Integrate(3log(x)dx)

y = 3x(log(x) - 1) + C

y = 3xlog(x) - 3x + C

Answer 2

dy/dx = log{x(x^2)}

dy/dx = logx^3

dy=[log x^3] dx

integrating both sides

int dy = int [log x^3] dx

y = xlogx^3 - 3x/ln10 + c

Therefore

y = 3xlogx - 3x/ln10 + c