a,
$\displaystyle\int (2x+3)dx$
$=\displaystyle\int 2xdx+\displaystyle\int 3dx$
$=x^2+3x+C$
b,
$\displaystyle\int (4x+1)dx$
$=\displaystyle\int 4xdx+\displaystyle dx$
$=2x^2+x+C$
c,
$\displaystyle\int (3x^2+2x+6)dx$
$=\displaystyle\int 3x^2dx+\displaystyle\int 2xdx+\displaystyle\int 6dx$
$=x^3+x^2+6x+C$
d,
$\displaystyle\int \left(e^x+\dfrac{1}{x+3}\right)dx$
$=\displaystyle\int e^xdx+\displaystyle\int \dfrac{dx}{x+3}$
$=e^x+\ln|x+3|+C$