integrate by parts the equation dy/dx = (3x-4)(2x^2+5).

The equation we use to integrate by parts is

y = uv - ∫ v(du/dx) dx + c

so we separate dy/dx into u=(3x-4) and dv/dx=(2x²+5)

however we still need to find du/dx and v,

by differentiating u (bring the power down, make the power one less) we can find du/dx therefore du/dx = 3

to integrate dv/dx we need to add one to the power then divide by the new power so v = 2/3x³+5x

we can then substitute all of our values into the equation:

y = (3x-4)(2/3x³+5x) - ∫ 3(2/3x³+5x) dx +c

y = (3x-4)(2/3x³+5x) - ∫ 2x³+15x dx +c

y = (3x-4)(2/3x³+5x) - (1/2x⁴+15/2x²) +c