Question

$\int\limits {(4x^{3}-\frac{2}{x^{2} } +7sinx )} \, dx$

Answer 1

$\int (4 {x}^{3} - \frac{2}{ {x}^{2} } + 7 \sin(x)) dx = 4\int {x}^{3} dx - 2 \int {x}^{ - 2} dx + 7 \int \sin(x) dx = \\ = \frac{4 {x}^{4} }{4} - 2( - {x}^{ - 1}) + 7( - \cos(x) ) = {x}^{4} + \frac{2}{x} - 7 \cos(x) + C$