Integral of a^x

The derivative of [1/(ln a)]⋅a^x is
[1/(ln a)]⋅[a^x (ln a)] = a^x.

derivative of a^x

And integral and derivative
are the opposite operations.

So the integral of a^x is
[1/(ln a)]a^x + C.

2^x(3^x - 1) = 6^x - 2^x

The integral of 6^x is
[1/(ln 6)]⋅6^x.

Write the coefficient -.

The integral of 2^x is
[1/(ln 2)]⋅2^x.

The given integral is an indefinite integral.
So write +C.

So [1/(ln 6)]⋅6^x - [1/(ln 2)]⋅2^x + C is the answer.