Integral of a root of a quantity, with u' present:

This is not like the patterns in any of out rules unless we convert the radical to a power:

Now it may fit the pattern of the General Power rule for integrals.

Try , n = 1/2, and

The only missing part is a factor of 30, which we can handle by using . Upon substitution, we get

Now we use the Scalar Multiple rule for integrals to get

Applying the General Power rule for integrals, we get

To finish the problem, we substitute u as a function of x:

Test Problem: Find

a)

b)

c)

d)