Consider this indefinite integral:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int(x^2+6)(2x)dx[/tex]

There are two ways I could approach solving it. The first one would be to multiply the terms, then solve using the sum rule. That approach would yield this solution:

[tex]\frac{x^4+12x^2}{2} + C[/tex]

The other way would be by substitution. It would yield this:

[tex]\frac{(x^2+6)^2}{2} + C[/tex]

The second constant is 18 less than the first one. I realize that since they're arbitrary constants, it might not matter, but I want to be clear. My question is:

Strictly speaking, are both solutions equally correct or is only one correct? If it's neither completely equal or one being the only correct answer, and it's merely a matter of preference, could you elaborate in what context which solution is preferable?

Thanks!

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# Is One or Both of the Integral Solutions Correct?

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