The graph of y = f(x) conforms to the slope field of the differential equation dy/dx = 4xlnx. Find f(x). (see attached)

Question

jennychan12 · Answer

attachment

jennychan12 · Answer

i tried using seperation of variables to find y,
dy = (4xlnx) dx
$$\int\limits dy = \int\limits (4xlnx)dx$$

whpalmer4 · Answer

Are you able to do the integrals?

jennychan12 · Answer

i don't know what's the integral of 4xlnx.
i did the integral of dy, which is just y.
i just don't know how to integrate 4xlnx. Would you use u-sub here?

whpalmer4 · Answer

integrate by parts...

jennychan12 · Answer

i don't think we've learned that yet :(

whpalmer4 · Answer

it may be what you call u-sub...

$$\int\limits_{}^{} u dv = uv - \int\limits_{}^{} v du$$

whpalmer4 · Answer

here I would do u = log x and dv = x dx

whpalmer4 · Answer

u = ln x, just to be clear

whpalmer4 · Answer

What did you get for your answer?

jennychan12 · Answer

yeah, thanks :)