Integral of the sum of reciprocals:

Since the Power rule for integrals applies when the power is in the numerator, we need to rewrite this in terms of negative powers:

Now we can use the Sum rule for integrals to get

Next use the Scalar Multiple rule for integrals to get

Finally we can use the Power rule for integrals to get

Test Problem: Find I:

a)

b)

c)

d)