Find the indefinite integral using integration by substitution: Sx^2 sqrt(x+1) dx i figured u=x+1, x=u-1, du=dx S sqrt u du (2/3)u^(3/2) +C (2/3)(x+1)^(3/2) +C
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Evaluate `int x^2sqrt(x+1)dx` :
If we use your substitution:
`u=x+1,du=dx,x=u-1` we can rewrite the integral as:
`int(u-1)^2u^(1/2)du`
`=int(u^2-2u+1)u^(1/2)du`
`=int(u^(5/2)-2u^(3/2)+u^(1/2))du`
The integral of a sum is the sum of integrals so:
`=2/7u^(7/2)-4/5u^(5/2)+2/3u^(3/2)+c_1`
Substituting...
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