Question

What is the Integral of 10^ln x dx?

Answer 1

`10^(\ln x)=e^{\ln 10^(\ln x)}=e^(\ln x\cdot\ln 10)=(e^(\ln x))^(\ln10)=x^(\ln10)`

So we have

`\displaystyle\int10^(\ln x)\,\mathrm dx=\int x^(\ln10)\,\mathrm dx}=(x^(1+\ln10))/(1+\ln10)+C`

which, as the above manipulation showed, is equivalent to

`(x10^(\ln x))/(1+\ln10)+C`