Calculate:
`(a)` `int(x^3-1/x+3x)dx` `(b)` `int(x^2+2)dx` ,

Options

A. `(x^(4)/(4)) - ln x + (3x^(2)/(2)) + C
` , `(x^(3)/(3)) + 2x + C`
B. `(x^(4)) - ln x + (3x^(2)/(2)) + C
` , `(x^(3)/(3)) + 2x + C`
C. `(x^(4)/(4)) - x^(-2) + C
` , `(x^(3)/(3)) + 2x + C`
D. `(x^(4)/(4)) - ln x + (3x^(2)/(2)) + C
` , `(x^(3)/(3)) + 2 + C`

Answer

A

Explanation

a. `int(x^2+2)dx=intx^2dx+int2dx=x^3/3+2x+c`
b. `int(x^3-1/x+3x)dx=intx^3dx-int1/xdx+int3xdx=x^4/4-logx+(3x^2)/(2)+c`
c. `int(x^(3//2)-x^(1//2)+5x)dx=intx^(3//2)dx-intx^(1//2)dx+int5xdx`
`=(2x^(5//2))/(5)-(2x^(3//2))/(3)+5/2x^2+c`
d. `int(e^(2x)+5)dx=inte^(2x)dx+int5dx=(e^(2x))/(2)+5x+c`