integral dari (2x+3)²dx dengan pembatas atas 4 dan pembatas bawah nol

Integral

[tex] \int ^4 _0 (2x+3)^2 ~ dx \\ \\ = \int ^4 _ 0 4x^2 + 12x + 9 ~ dx \\ = \frac{4}{2+1} x^{2+1} + \frac{12}{1+1} x^{1+1} + \frac{9}{0+1} x^{0+1} + C \right | ~~~~^4 _0 \\\\ = \frac{4}{3} x^3 + 6x^2 + 9x + C ~~~~^4 _ 0 \\\\ = (\frac{4}{3} (4)^3 + 6 (4)^2 + 9(4) + C ) - (\frac{4}{3} (0)^3 + 6(0)^2 + 9(0) + C) \\\\ = (\frac{256}{3} + 96 + 36 + C - C) \\\\ = \frac{652}{3} \rightarrow 217 \frac{1}{3} [/tex]