first make a substitution and then use integration by parts to evaluate the integral. (use c for the constant of integration.) x ln(5 + x) dx

Step-by-step explanation:

Ok, so we start by setting the integral up. The integral we need to solve is:

so according to the instructions of the problem, we need to start by using some substitution. The substitution will be done as follows:

U=5+x

du=dx

x=U-5

so when substituting the integral will look like this:

now we can go ahead and integrate by parts, remember the integration by parts formula looks like this:

so we must define p, q, p' and q':

p=ln U

q'=U-5

and now we plug these into the formula:

Which simplifies to:

Which solves to:

so we can substitute U back, so we get:

and now we can simplify:

notice how all the constants were combined into one big constant C.

4

step-by-step explanation:

6 (donuts) divided by 3 is 2.

so 2/3 means 2 times 2, which is 4/6.

you get two and your friend gets four.

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,