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" The evaluation of "int(px^(p+2q-1)-qx^...

" The evaluation of "int(px^(p+2q-1)-qx^(q-1))/(x^(2p+2q)+2xp+q+1)dx" is "

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int(px^(p+2q-1)-qx^(q-1))/(x^(2p+2q)+2x^(p+q)+1)dx

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

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

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

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    

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    

int((p+q tan^(-1)x))/(1+x^(2))dx

If x nearly equal to 1 show that (px^p - qx^q)/(p-q) = x^(p+q) (nearly)

If x nearly equal to 1 show that (px^p - qx^q)/(p-q) = x^(p+q) (nearly)