The discussion revolves around finding the antiderivative of a function involving a polynomial and a square root. Participants are examining their solutions against a textbook answer and exploring the validity of their approaches.
Some participants assert that the textbook solution is correct while others express uncertainty about their own solutions. There is an ongoing examination of specific mistakes in the original poster's approach, particularly regarding the expansion of terms.
Participants note the importance of verifying their solutions by differentiation and mention specific algebraic rules that may have been misapplied. There is a reference to external tools for checking integrals, indicating a reliance on additional resources for validation.
Differentiate your solution. Is the result you get equal to the integrand? If so, your work is correct.Anti Hydrogen said:the book shows a solution that i m not getting
https://es.symbolab.com/solver/integral-calculator/\int x^{2}\sqrt{a+bx}dxMath_QED said:Your book is right:
https://www.wolframalpha.com/input/?i=integral+u^2*(a+bu)^(1/2)+du
First mistake I saw in your solution is that you forgot the factor ##2## in the rule ##(a+b)^2 = a^2 + 2ab + b^2## while expanding ##((v-a)/b)^2##. I did not read further so it may contain further mistakes.