5. Jika F'(x)=3x² + 6x / x dan F(-1) = 2, maka F(x) = ........

5. Jika F'(x)=3x² + 6x / x dan F(-1) = 2, maka F(x) = ……..

$f'(x) = frac{3 {x}^{2} + 6x }{x} \ f'(x) = 3x + 6 \ f(x) = int(3x + 6)dx \ f(x) = frac{3}{1 + 1} {x}^{1 + 1} + frac{6}{0 + 1} {x}^{0 + 1} + c \ f(x) = frac{3}{2} {x}^{2} + 6x + c \ f( - 1) = frac{3}{2} {( - 1)}^{2} + 6( - 1) + c \ 2 = frac{3}{2} - 6 + c \ c = 8 - frac{3}{2} \ c = frac{16 - 3}{2} \ c = frac{13}{2}$

$f(x) = frac{3}{2} {x}^{2} + 6x + frac{13}{2}$