The discussion focuses on finding the indefinite integral of the function \(\int \frac{x^{1/3}}{x^{1/3}+1}dx\) using u-substitution. The substitution defined is \(u = x^{1/3}\), leading to \(du = \frac{1}{3x^{2/3}}dx\). Participants clarify that the numerator transforms into \(u^3\) due to the relationship between \(x\) and \(u\), specifically that \(x = u^3\). This understanding is crucial for correctly evaluating the integral.
PREREQUISITESStudents studying calculus, particularly those focusing on integration techniques, as well as educators looking for examples of u-substitution applications.
csc2iffy said:Homework Statement
\int(x^(1/3)/(x^(1/3)+1))dxHomework Equations
I know I have to use u substitution
u=x^(1/3)
du=1/(3x^(2/3))dxThe Attempt at a Solution
I know that the denominator of the equation will be u+1, but I don't understand how to find the numerator because I thought it would just be u, but wolfram alpha says it's u^3?