Integrate 9^x

To integrate 9^x, also written as ∫ 9^x dx, we first recognise that this is an exponential and will require the base change technique.

At this step, we change the base as shown above.

We take log to the base e on both sides.

At this step, we find that lne=1, which simplifies the above expression.

We now have an expression for z.

We substitute for z in the expression 9^x=e^z to give the above expression.

As you can see, we now have a simpler integration, which is the same thing.

We integrate the simpler version, where C is the integration constant.

Since e^xln9=9^x, which we found earlier, we can substitute that to give the above expression.

Finally, this is the result.