Integrate the function

f$($x$)=(2+2$x$+$x$3)$dx$.$f$($x$)=(2+2$x$+$x$3)$dx$.$

a$.$

$2$x$+$x$2+$x$44+$C$2$x$+$x$2+$x$44+$C

b$.$

$2$x$+$x$2+$x$442$x$+$x$2+$x$44$

c$.$

$2+3$x$2+$C$2+3$x$2+$C

d$.$

$2+3$x$22+3$x$2$

e$.$

None of the given options is correct.