`intx^(3)sqrt(x^(2)-4)dx` का मान ज्ञात कीजिए ।

Explanation

माना `I=intx^(3)sqrt(x^(2)-4)dx`
`" "=intx^(2)sqrt(x^(2)-4).(x.dx)`
माना `" "x^(2)-4=t`
`rArr" "2x=(dt)/(dx)`
`rArr" "x.dx=(dt)/(2)`
`therefore" "I=int(t+4)sqrtt.(dt)/(2)`
`" "=(1)/(2)int(t^(3//2)+4t^(1//2))dt`
`=(1)/(2)[(2)/(5)t^(5//2)+(8)/(3)t^(3//2)]+c`
`" "=(1)/(5)(x^(2)-4)^(5//2)+(4)/(3)(x^(2)-4)^(3//2)+c`