The discussion revolves around the integral of the function \(x^2 \sqrt{x^3 + 1}\) with respect to \(x\). Participants are examining the correctness of an integration attempt using substitution.
The discussion is active, with participants affirming the method used and emphasizing the importance of differentiation as a verification step. There is a focus on ensuring completeness in the solution, particularly regarding the constant of integration.
Participants are discussing the integral in the context of homework help, indicating a learning environment where verification and thoroughness are encouraged.
Lo.Lee.Ta. said:∫x^2(√(x^3 + 1))
u = x^3 + 1
du = 3x^2dx
(1/3)du = x^2dx
∫√(u)*(1/3)du
= 2/3(u)^3/2 *(1/3)
= 2/9(x^3 + 1)^3/2
Is this the correct answer? Thank you.
Lo.Lee.Ta. said:Thanks, you guys! :)
That's true. I should differentiate when I'm not sure...