Your idea is correct! But you got the integra wrong for v'(z) (you forgot a
minus sign!). The correct one is:

`v(z)=-10^(-z)/ln(10)`

You can check that this is the correct v(z) by taking its derivative with
respect to z. You got it right with u(z) and u'(z), so I will use then for the
integration by parts.

Now, following the integration by parts we have:

`intu(z)v'(z)=u(z)v(z) - intu'(z)v(z)`

Inserting our functions:

`intz/10^z = -z10^(-z)/ln(10) - int(-10^(-z)/ln(10))=`

`= -z10^(-z)/ln(10) + int10^(-z)/ln(10)`

All that remains is to evaluate the integral of `10^(-z)/ln(10)`

But we know that integral. It is simply `10^(-z)/(ln^2(10)) + C`

Thus, we get as a final result:

`intz/10^z = -z10^(-z)/ln(10) - 10^(-z)/(ln^2(10)) + D`

I used D for constant because that may not be the same value as C, due to
the integral being indefinite on the first term aswell!

I believe your problem was with the minus sign, which could have resulted in a
really complicated integral.

` `

` `

## See eNotes Ad-Free

Start your **48-hour free trial** to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Already a member? Log in here.