Integration of : constant needed:

This looks like a quantity raised to a power times the derivative of the quantity. Let's try the General Power rule for integrals:
Let , n = 8, .

Since only x is present as a factor, the last equation allows us to replace x by .

Now the integral becomes

We now use the Scalar Multiple rule for integrals to get

Now we can use the General Power rule for integrals to get

Finally we substitute for u (as we defined it above) to get an answer in terms of x:

Test Problem: Find

a)

b)

c)

d)