It is a matter of integrating f′:
[tex]f(x)=\int \sqrt{x}(6+10x)dx,
\\
\\f(x)=\int 6x^{1/2}dx+\int10x^{3/2}dx,
\\
\\f(x)=4x^{3/2}(x+1)+C.
[/tex]
Combine the constants. Then use the initial condition to find C:
[tex]11=8+C\implies C=3[/tex]
Therefore,
[tex]f(x)=4x^{3/2}(x+1)+3.[/tex]
