Question

\int 2^{2x}\cdot 5^x dx

Answer 1

$2^{2x}\cdot 5^x=4^x\cdot 5^x=20^x$

$\int 2^{2x}\cdot 5^xdx=\int 20^xdx=\int e^{x\ln 20}dx=$

$=\frac{1}{\ln 20}\int e^{x\ln 20}d(x\ln 20)=\frac{1}{\ln 20}e^{x\ln 20}+C=$

$=\frac{1}{\ln 20}20^x+C$

Answer: $\frac{1}{\ln 20}20^x+C$