Answer
The first term of the answer, $\displaystyle \frac{2^{x+1}}{x+1}$, is incorrect.
Correct answer:$\displaystyle \qquad \frac{2^{x}}{\ln 2}-x+C$
Work Step by Step
$\displaystyle \int(2^{x}-1)dx=\int 2^{x}dx-\int 1dx=$
Term by term:
$\displaystyle \int 2^{x}dx=\qquad$ applying $\displaystyle \int b^{x}dx=\frac{b^{x}}{\ln b}+C$ $\displaystyle \quad=\frac{2^{x}}{\ln 2}+C$
the first term of the answer, $\displaystyle \frac{2^{x+1}}{x+1}$, is incorrect.
$-\displaystyle \int 1dx=-x+C$
the last two terms are correct.
Correct answer:$\displaystyle \qquad \frac{2^{x}}{\ln 2}-x+C$
