Evaluate: `int(x^2-1)/(x^4+1)\ dx`

Explanation

According to the question,
`S={(H,H),(H,T),(T,1),(T,2),(T,3),(T,4),(T,5),(T,6)}`
In the above set, there are 8 elementry events, but all are not equally likely.
However, events (H,H) and (H,T) are equally likely. Each event has pobability `1/4.`
Events `(T,1),(T,2),....(T,6)` are equally likely and each event has probability `1/12.`
Let event A be "the dice shows a number greater than 4" And event B be "there is at least one tail"'.
`thereforeA={(T,5),(T,6)}`
and `B={(H,T),(T,1),(T,2),(T,3),(T,4),(T,5),(T,6)}`
`thereforeAnnB={(T,5),(T,6)}`
`therefore"Required probability,"P(A//B)=(P(AnnB))/(P(B))`
`=(1/12+1/12)/(1/4+1/12+1/12+1/12+ 1/12+ 1/12+1/12)=(1//6)/(3//4)=2/9`