Question

How do you integrate `int ln(e^(2x-1))dx`?

Answer 1

`x^2 - x +c`

Explanation:

Use knowledge of logarithms

`log_a a^f(x) -= f(x) ln_a a -= f(x)`

Hence `ln e^f(x) -= f(x)`

`=> int ln (e^(2x-1) ) dx = int (2x-1) dx`

Use the reverse power rule:

`= x^2 -x + c`