[tex] \int( \frac{4}{3} {x}^{3} - \frac{3}{4} {x}^{2} + 5) \: dx[/tex]
[tex] = \int \frac{4}{3} {x}^{3} \: dx - \int \frac{3}{4} {x}^{2} \: dx + \int5 \: dx[/tex]
[tex] = \frac{4}{3} \int {x}^{3} \: dx - \frac{3}{4} \int {x}^{2} \: dx + 5 \int1 \: dx[/tex]
[tex] = \frac{4}{3} \times \frac{ {x}^{3 + 1} }{3 + 1} - \frac{3}{4} \times \frac{ {x}^{2 + 1} }{2 + 1} + 5x[/tex]
[tex] = \frac{4}{3} \times \frac{ {x}^{4} }{4} - \frac{3}{4} \times \frac{ {x}^{3} }{3} + 5x[/tex]
[tex] = \frac{ {x}^{4} }{3} - \frac{ {x}^{3} }{4} + 5x + C[/tex]
