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.

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

$4034.40

the perimeter of the field is the sum of the lengths of the four sides:

47 yd + 158 yd + 47 yd + 158 yd = 410 yd

the cost of 3 ft (1 yd) of fence is 3×$3.28 = $9.84.

so the cost of jake's wood perimeter fance is

(410 yd) × ($9.84 /yd) = $4034.40