Integrate the following functions with respect to `x`
`int (5x^2 + 3x -2) dx`

Options

A. `(5x^2)/(3) + (3x^(2))/ (2) - 2x + c`
B. `(x^3)/(3) + (3x^(2))/ (2) - 2x + c`
C. `(5x^3)/(3) + (3x^(2))/ (2) - 2x + c`
D. `(5x^3)/(3) + (x^(2))/ (2) - 2x + c`

Answer

C

Explanation

(a) `int (5x^(2) + 3x - 2) dx = 5 int x^(2) dx + 3 int x dx -2 int dx`
= `(5x^3)/(3) + (3x^(2))/ (2) - 2x + c`
(b) `int (4sin x -(2)/(x)) dx =4 int sin x dx - 2 int (dx)/ (x)`
= `-4 cos x - 2 ln x + c`
(c ) `int (dx)/(4x+5) = (1)/(4) int (dX)/(X) , where X =4x+5`
= `(1)/(4) In X + c_1 = (1)/(4) In (4x + 5 ) + c_(2)`
(d) `int ( 6x + 2 )^(3) dx = (1)/ (6) int X^(3) dX , where X = 6x + 2`
`( 1)/(6) ((X^(4))/(4)) + c_(1) = ( 6x + 2 ) ^ (4)/ (24) + c_(2)`