Answer to Question #132619 in Calculus for qwerty

Question

\int 3^{x+1} dx

Answer 1

$\int 3^{x+1}dx=\int e^{(x+1)\ln 3}dx=\int e^{(x+1)\ln 3}d(x+1)=$

$=\frac{1}{\ln 3}\int e^{(x+1)\ln 3}d((x+1)\ln 3)=\frac{1}{\ln 3}e^{(x+1)\ln 3}+C=$

$=\frac{1}{\ln 3}3^{x+1}+C$

Answer: $\frac{1}{\ln 3}3^{x+1}+C$