Question

integral 3^x+2 dx

Answer 1

\[\int 3^{x+2}~dx~\text{ or }~\int(3^x+2)~dx~?\]

Answer 2

If the first one, you have \(3^{x+2}=3^x\cdot3^2=9(3^x)\). In either case, you have to find the integral
\[\int 3^x~dx\]

Answer 3

\[\large3^x=e^{\ln 3^x}=e^{x\ln 3}\]
\[\int e^{x\ln3}~dx\]
Let \(u=x\ln 3\), so that \(du=\ln3~dx~\iff~\dfrac{1}{\ln3}du=dx.\)
\[\frac{1}{\ln3}\int e^u~du\]

Answer 4

thanks it was the first one . ..

Answer 5

which means you have to factor out the 9. Don't forget to sub back.