`int(cosx+xsinx)/(x^(2)+xcosx)dx= ` . . . .

Options

A. `logabs((xsinx)/(x+cosx))+c`
B. `logabs((x)/(x+cosx))+c`
C. `logabs(cosx+xsinx)+c`
D. `logabs(x^(2)+xcosx)+c`

Answer

B

Explanation

`int(cosx+xsinx)/(x^(2)+xcosx)`dx
`=int(cosx+xsinx+x-x)/(x(x+cosx))`dx
`=int((cosx+x)+x(sinx-1))/(x(x+cosx))`dx
`=int1/xdx+int(sinx-1)/(x+cosx)dx`
`=logabsx-int(1-sinx)/(x+cosx)dx`
`=logabsx-log(x+cosx)+c`
`=logabs(x/(x+cosx))+c`