integration of 1^x

Hi Heurka,

I don't get what you did all that for?

Why is it reasonable to set 

$$1^x=e^{x\times ln(1)}$$

I mean I know that

$$1^x=1$$

that is where i started but I do not understand why you put those lines of working in front of it.  

1^ any real number = 1

So  1^x=1

The integral of 1 is x+c

I think that is the answer 

integration of 1^x

$$\int{1^x}\ dx \ ?$$

   $$\begin{array}{llr} set & \quad 1^x=e^ { x \times \ln{(1)} } & \qquad \ln{(1)} = 0\\ so & \quad 1^x=e^ { x \times 0} & \qquad x\times0= 0\\ so & \quad 1^x=e^0 & \qquad e^0=1\\ so & \quad 1^x=1 \end{array} \\ \int{1^x}\ dx = \int{1}\ dx = x + c$$

Hi Melody,

it is not reasonable to set  $$1^x=e^{x\times ln(1)}$$ ,

but in general it is easier to integrate $$e^x$$