Answer
a) $\frac{3^{x}}{\ln(3)}+C $
b) $-\frac{2^{-x}}{\ln(2)}+C $
c) $\frac{(\frac{5}{3})^{x}}{\ln(\frac{5}{3})}+C $
Work Step by Step
Recall: $\int a^{x}dx=\frac{a^{x}}{\ln(a)}$
Use this formula to obtain the results below:
a) $\int3^{x}dx=\frac{3^{x}}{\ln(3)}+C $
b) $\int2^{-x}dx=\int(\frac{1}{2^{x}})dx=\int(\frac{1}{2})^{x}dx $
$=\frac{(\frac{1}{2})^{x}}{\ln(\frac{1}{2})}+C=\frac{\frac{1}{2^{x}}}{\ln(1)-\ln(2)}$
$=\frac{2^{-x}}{0-\ln(2)}+C=-\frac{2^{-x}}{\ln(2)}+C $
c) $\int(\frac{5}{3})^{x}dx=\frac{(\frac{5}{3})^{x}}{\ln(\frac{5}{3})}+C $
