The discussion revolves around the integration of the function \(\int (\arcsin x)^{2} dx\) using integration by parts and substitution techniques. Participants detail the steps involved, including setting \(u = \arcsin x\) and \(dv = dx\), leading to the expression \(x \arcsin x - \int \frac{x}{\sqrt{1-x^{2}}} dx\). The conversation highlights the necessity of multiple rounds of integration by parts and the application of substitutions such as \(u = 1 - x^{2}\) to simplify the integral. Ultimately, the correct approach requires careful tracking of terms and signs throughout the integration process.
PREREQUISITESStudents and educators in calculus, particularly those focusing on integration techniques, as well as anyone seeking to deepen their understanding of inverse trigonometric functions and their applications in integration.
iRaid said:I see it, thanks. But I would probably never think of that lol.
Dick said:Well, I didn't either. Don't feel bad.