Integrating exponential function beside e^x

Question

I am doing a math assignement where I find the area of a country using functions. I used an exponential equation that was not a base of e. I was able to integrate it using a calculator, but I wanted to know if there was a method to integrate these functions similar to that of e^x.

Would there be a way to integrate an exponential function such as 2 . 4^x-5-10? Where it is an exponential but not an e^x exponential.

Any help would be appreciated,

Cheers.

Answer 1

d/dx (a^x) = a^x ln(a)

This is because a^x = e^aln(x) d/dx of that is e^alnx ln(a) = a^xlna

This leads to the conclusion that int(a^xdx) = a^x/ln(a) (think anti-derivative)

Int(2.4^x-5) dx = 2.4^x-5/ln(2.4)