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

Explanation

`int_(2)^(4)(x^(2)+x)/(sqrt(2x+1))dx=[(x^(2)+x)int(1)/(sqrt(2x+1))dx]_(2)^(4)-int_(2)^(4)(d)/(dx)(x^(2)+x)int(1)/(sqrt(2x+1))dx`
`=[(x^(2)+x)sqrt(2x+1)]_(2)^(4)- int_(2)^(4)(2x+1)sqrt(2x+1)dx`
`=(60-6sqrt5)-int_(2)^(4)(2x+1)^(3//2)dx`
`=(60-6sqrt5)-(1)/(5)[(2x+1)^(5//2)]_(2)^(4)`
`=(60-6sqrt5)-(1)/(5)[243-(5)^(5//2)]`
`=(60-6sqrt5)-(1)/(5)[243-25sqrt5]`
`=(57-5sqrt5)/(5)`