Solve: (dy)/(dx) = {x}^(3) + 5x - 18 ​

Question

Solve:

`(dy)/(dx) = {x}^(3) + 5x - 18`
​

Answer 1

`y = (1)/(4) {x}^(4) + (5)/(2) {x}^(2) - 18x + k`

Explanation:

`dy = ( {x}^(3) + 5x - 18)dx`

Integrating the above expression, we get

`y = \int( {x}^(3) + 5x - 18)dx`

`= (1)/(4) {x}^(4) + (5)/(2) {x}^(2) - 18x + k`

where k is the constant of integration