- #1
DocZaius
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Consider this indefinite integral:
[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!
[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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