`int (px^(p+2q-1)-qx^(q-1))/(x^(2p+2q)+2x^(p+q)+1) dx` is equal to (1)   `-x^p/(x^(p+q)+1)+C`    (2)   `x

Question

`int (px^(p+2q-1)-qx^(q-1))/(x^(2p+2q)+2x^(p+q)+1) dx` is equal to
(1)   `-x^p/(x^(p+q)+1)+C`    (2)   `x^q/(x^(p+q)+1)+C`   
(3)   `-x^q/(x^(p+q)+1)+C`    (4)   `x^p/(x^(p+q)+1)+C`   
A. ` -(x^(p))/(x^(p+q)+1)+C`
B. ` (x^(q))/(x^(p+q)+1)+C`
C. ` -(x^(q))/(x^(p+q)+1)+C`
D. ` (x^(p))/(x^(p+q)+1)+C`

Answer 1

Correct Answer - C
`int(px^(p+2q-1)-qx^(q-1))/((x^(p+q)+1)^(2))dx=int(px^(p-1)-qx^(q-1))/((x^(p)+x^(-q))^(2))dx " " ("Dividing "N^(r)" and "D^(r) " by "x^(2q))`
`=int(dt)/(t^(2))= -(1)/(t)+C, " where " t=x^(p)+x^(-q)`
`= - (1)/(x^(p)+x^(-q))+C`
`= -(x^(q))/(x^(p+q)+1)+C`