- #1

1MileCrash

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## Homework Statement

[itex]\int (x+1)^2 dx[/itex]

## Homework Equations

## The Attempt at a Solution

I am just getting into this, and this is a simple problem, but my book and I took two separate routes. My question, essentially, is does any constant you get just "combine" with the "any constant" C?

I went with:

[itex]\int (x+1)^2 dx = \int x^2+2x+1 dx[/itex]

Which yields

[itex]\frac{1}{3}x^3+x^2+x+C[/itex]

Now, my textbook took a wildly different method, with u substitution and arrived at:

[itex]\frac{(x+1)^3}{3}+C[/itex]

These equations are

*not*identical, but their derivatives

*are.*So, they are both solutions and they are both the same. My gripe with the textbook solution is that, their answer can be brought to mine but with another constant. Why would they do that?

[itex]\frac{(x+1)^3}{3}+C[/itex]

[itex]=\frac{x^3+x^2+3x+1}{3}+C[/itex]

[itex]\frac{1}{3}x^3+x^2+x + \frac{1}{3} + C[/itex]

Why would they give that as a final result? Their answer is just mine with another constant hidden in. Is there are reason for them to do that?