If `int(1)/(x^(3)+x^(4))dx=(A)/(x^(2))+(B)/(x)+log|(x)/(x+1)|+C` , then

Options

A. `A=1/2,B=1`
B. `A=1,B=-1/2`
C. `A=-1/2,B=1`
D. `A=1,B=1`

Answer

C

Explanation

`int(dx)/(x^(4)+x^(3))=int((x+1)-x)/(x^(3)(x+1))dx`
`=int(1/(x^(3))-1/(x^(2)(x+1)))dx`
`int(1/(x^(3))-1/(x^(2))+1/(x(x+1)))dx`
`=int(1/(x^(3))-1/(x^(2))+1/x-1/(x+1))dx`
`=-1/(2x^(2))+1/x+log|x|-log|x+1|+c`
`=-1/(2x^(2))+1/x+log|x/(x+1)|+C`
`:.A=-1/2` and `B=1`