Evaluate: `intx^2sqrt(1+x)dx`

Explanation

Given:

`intx^2sqrt(1+x)dx`

`I=intx^2sqrt(1+x)dx`

Let `1+x=t implies dx=dt` and `x=t-1`

Then

`I=int(t-1)^2sqrttdt`

`I=int(t^2+1-2t)sqrttdt`

`I=int[t^(5/2)+t^(1/2)-2t^(3/2)]dt`

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