Question

Solve
${\int }_0^4(x+e^{2x})dx$

Answer 1

${\int }_0^4(x+e^{2x}dx)$

${\int }_0^{4}xdx+{\int }_0^4{e}^{2x}dx$

$[\frac{x^2}{2}{]}_0^4+[\frac{e^{2x}}{2}{]}_0^4$

$\frac{1}{2}[16-0]+\frac{1}{2}[e^8-e^0]$

$\frac{16}{2}+\frac{e^8}{2}-\frac{1}{2}$

$\frac{e^8}{2}-\frac{15}{2}$

$\frac{1}{2}(e^8-15)$