The problem involves finding all primitive functions (antiderivatives) for the function 2x(x^2+3)^4, which falls under the subject area of calculus, specifically integration techniques.
Some participants have suggested using substitution as a potential approach to simplify the integration process. There is an acknowledgment of the need for a constant of integration and a hint that a simple substitution could be effective. Multiple interpretations of the problem are being explored, but no consensus has been reached.
Participants note that the problem may have been misclassified initially and that it requires a specific integration technique rather than straightforward expansion. There is also a reminder to consider the highest degree term in the final answer.
I have moved this thread, as it is not a precalculus problem.beyondlight said:Homework Statement
Determine all primitive functions for the function:
2x(x^2+3)^4
2. The attempt at a solution
When i expanded i got the primitive to be:
2(x^9/9)+3x^8+18x^6+54x^4+81x^2But this was wrong. I am not sure I have understood the question. Help?
If z = x^2 + 3, what is dz?beyondlight said:One possible substitution is 2x(z)^4
A very simple substitution will work, and you're on the right track,beyondlight said:But I am not sure how to proceed from here...