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

Expert Answers

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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:




The integral of a sum is the sum of integrals so:


Substituting for u we get:


`=2/7(x+1)^(7/2)-4/5(x+1)^(5/2)+2/3(x+1)^(3/2)+C` ***********************


This can be rewritten; factor out the common `(x+1)^(3/2)` and a common fraction `2/105` to get:




`=2/105(x+1)^(3/2)[15x^2-12x+8]+C` *************************


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