Question

Интеграл(2^x * e^x)dx

Answer 1

$\displaystyle\int2^x*e^xdx=\int(2e)^xdx=\frac{(2e)^x}{ln(2e)}+C\\\\\\\int2^x*e^xdx=2^x*e^x-ln2\int 2^x*e^xdx\\(1+ln2)\int2^x*e^xdx=2^x*e^x\\\int2^x*e^xdx=\frac{2^x*e^x}{1+ln2}+C\\\\\\u=2^x;du=2^xln2dx\\dv=e^xdx;v=e^x$