Answer
\[\frac{2^x}{\ln 2}+\frac{5^x}{\ln 5}+C\]
Where $C$ is constant of integration
Work Step by Step
Let \[I=\int\frac{4^x+10^x}{2^x}dx\]
\[\Rightarrow I=\int\frac{2^{2x}+2^x5^x}{2^x}dx\]
\[\Rightarrow I=\int (2^x+5^x)dx\]
We will use the formula \[\int a^x\,dx=\frac{a^x}{\ln a}\;\;\;...(1)\]
Using (1)
\[I=\frac{2^x}{\ln 2}+\frac{5^x}{\ln 5}+C\]
Where $C$ is constant of integration
Hence,
\[\int\frac{4^x+10^x}{2^x}dx=\frac{2^x}{\ln 2}+\frac{5^x}{\ln 5}+C\]
