Question

$integrala \: \frac{4}{ \times } { \times }^{3} - \frac{3}{4} { \times }^{2} + 5 \: dx$

Answer 1

$\int( \frac{4}{3} {x}^{3} - \frac{3}{4} {x}^{2} + 5) \: dx$

$= \int \frac{4}{3} {x}^{3} \: dx - \int \frac{3}{4} {x}^{2} \: dx + \int5 \: dx$

$= \frac{4}{3} \int {x}^{3} \: dx - \frac{3}{4} \int {x}^{2} \: dx + 5 \int1 \: dx$

$= \frac{4}{3} \times \frac{ {x}^{3 + 1} }{3 + 1} - \frac{3}{4} \times \frac{ {x}^{2 + 1} }{2 + 1} + 5x$

$= \frac{4}{3} \times \frac{ {x}^{4} }{4} - \frac{3}{4} \times \frac{ {x}^{3} }{3} + 5x$

$= \frac{ {x}^{4} }{3} - \frac{ {x}^{3} }{4} + 5x + C$