`int_(0)^(1) (x^(4)+1)/(x^(2)+1)dx` का मान ज्ञात कीजिएः।

Explanation

यहाँ `I=underset(0)overset(1)int (x^(4)+1)/(x^(2)+1)dx`
`=underset(0)overset(1)int ((x^(4)+1)+2)/((x^(2)+1))dx`
`=underset(0)overset(1)int (x^(4)-1)/(x^2+1)dx +underset(0)overset(1)int (2)/(x^(2)+1)dx`
`=underset(0)overset(1)int ((x^2-1)(x^(2)+1))/((x^(2)+1))dx+2underset(0)overset(1)int (1)/(1+x^(2))dx`
`=[(x^(3))/(3)-x]_(0)^(1)+2[tan^(-1)x]_(0)^(1)`
`=(1/3-1)+2[tan^(-1)1-0]`
`=-2/3 2 pi/4=(3pi-4)/(6)`