Select all expressions matching the value of indefinite integral int (e^u+((1)/(2))^x)dx e^ux+(0.5^x)/(ln0.5)+C e^ux-(2^-x)/(ln0.5)+C glasshouse e^ux-(2^-x)/(ln2)+C

The correct answer is:<br />$e^{u}x-\frac {2^{-x}}{ln2}+C$<br /><br />Explanation:<br />The indefinite integral $\int (e^{u}+(\frac {1}{2})^{x})dx$ can be evaluated by integrating each term separately.<br /><br />For the first term, $\int e^{u}dx$, the integral is $e^{u}x$.<br /><br />For the second term, $\int (\frac {1}{2})^{x}dx$, we can rewrite it as $\int 2^{-x}dx$. The integral of $2^{-x}$ is $-\frac {2^{-x}}{ln2}$.<br /><br />Therefore, the correct expression for the indefinite integral is $e^{u}x-\frac {2^{-x}}{ln2}+C$.