Integrate 7^x
To integrate 7^x, also written as ∫ 7x 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 7^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^xln7=7^x, which we found earlier, we can substitute that to give the above expression.
Finally, this is the result.