Question

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

Answer 1

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

Answer 2

Are you able to do the integrals?

Answer 3

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?

Answer 4

integrate by parts...

Answer 5

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

Answer 6

it may be what you call u-sub...

\[\int\limits_{}^{} u dv = uv - \int\limits_{}^{} v du\]

Answer 7

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

Answer 8

u = ln x, just to be clear

Answer 9

What did you get for your answer?

Answer 10

yeah, thanks :)