The integral \(\int \frac{1}{x^2+1} dx\) can be solved using trigonometric substitution, specifically by letting \(x = \tan(u)\). This substitution simplifies the integrand to \(\int \sec^2(u) du\), which directly integrates to \(u + C\). The final result is \(\tan^{-1}(x) + C\). Attempts using ordinary substitution or partial fractions are ineffective for this integral.
PREREQUISITESStudents studying calculus, particularly those focusing on integration techniques, as well as educators looking for effective methods to teach integral calculus concepts.
Your first thought led you to try an ordinary substitution, u = x^2 + 1. This won't work, though, because du = 2xdx, so there's no way to change the given integrand to du/u.thereddevils said:Homework Statement
evaluate [tex]\int \frac{1}{x^2+1} dx[/tex]
Homework Equations
The Attempt at a Solution
This can't be [tex]\frac{\ln x^2+1}{2x}[/tex] , my first thought on this .
Then , i tried partial fraction , it didn't work either .