Answer
a) $\frac{x^{2}}{2}+\frac{2^{-x}}{\ln (2)}+C $
b) $\frac{x^{3}}{3}+\frac{2^{x}}{\ln(2)}+C $
c) $\frac{\pi^{x}}{\ln(\pi)}-\ln|x|+C $
Work Step by Step
a) $\int (x-(\frac{1}{2})^{x})dx=\int xdx-\int(\frac{1}{2})^{x}dx $
$=\frac{x^{2}}{2}-\frac{(\frac{1}{2})^{x}}{\ln (\frac{1}{2})}+C $
$=\frac{x^{2}}{2}-(-\frac{2^{-x}}{\ln (2)})+C $
$=\frac{x^{2}}{2}+\frac{2^{-x}}{\ln (2)}+C $
b) $\int(x^{2}+2^{x})dx=\int x^{2}dx+\int2^{x}dx $
$=\frac{x^{3}}{3}+\frac{2^{x}}{\ln(2)}+C $
c) $\int(\pi^{x}-x^{-1})dx=\int \pi^{x}dx-\int x^{-1}dx $
$=\frac{\pi^{x}}{\ln(\pi)}-\ln|x|+C $
