`int(x^(2)dx)/(sqrt(x+2))`का मान ज्ञात कीजिये |

Explanation

माना ` I = int(x^(2)dx)/(sqrt((x+)))" "....(1)`
माना `x + 2 = t rArr x = t - 2`
तथा `dx = dt`
अतः समी से `I = int((t-2))/((t)^(1//2)) = int ((t^(2) - 4t + 4)/(t^(1//2)))dt`
` = int(t^(3//2) -4t^(1//2) + 4t^(-1//2))dt `
`= (2)/(5)t^(5//2) - (8)/(3)t^(3//2) + 8t^(1//2)`
`= (2)/(5)(x+2)^(5//2) - (8)/(3)(x+2)^(3//2)+8(x+2)^(1//2)`