∫1x2(1+x2) dx= -1+x2x+C
ii) By applying the quotient, the sum, and the power rule for differentiation; verify the formula.
By applying quotient, the sum, and the power rule of derivative,
= -x· 121+x2-12·ddx1+x2- 1+x2x2
= -x22x 1+x2-12-1+x2x2
Multiply and divide the above expression by 1+x2,
= -x22x 1+x2-12-1+x2x21+x21+x2
After simplifying we get
Hence, the formula has been verified.