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Evaluate : int1^4(x^2+x)/(sqrt(2x+1))dx...

Evaluate : `int_1^4(x^2+x)/(sqrt(2x+1))dx`

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