Question

How do I evaluate `intz/e^(3z) dz`?

Answer 1

I would first write your integral in a more friendly form:
`intz/(e^(3z))dz=intz*e^(-3z)dz`

I would then use integration by parts:
Where you have:
`intf(z)*g(z)dz=F(z)*g(z)-intF(z)*g'(z)dz`

Where:
`F(z)=intf(z)dz`
`g'(z)` is the derivative of `g(z)`

In your case you can choose:
`f(z)=e^(-3z)`
`g(z)=z`
And:
`intz*e^(-3z)dz=z*e^(-3z)/(-3)-int1*e^(-3z)/(-3)dz=`
`=z*e^(-3z)/(-3)-e^(-3z)/9+c`