1. The problem statement, all variables and given/known data The integral of 5/(x^2 + 1) dx from -1 to 1. (The TheIntegral.jpg attachment shows this in a aesthetically-pleasing way.) 2. Relevant equations sin^2 (θ) + cos^2 (θ) = 1 1 + tan^2 (θ) = sec^2 (θ) cot^2 (θ) + 1 = csc^2 (θ) x = tan(θ) x = cot(θ) 3. The attempt at a solution When I am solving the integral, I successfully compute it using the x = tan(θ) substitution but when I use the x = cot(θ) substitution, I get the wrong answer. My specific work is attached as MyWork.jpg. The work in black is the work I got correct (as indicated by the red writing) and, the work in green is the work I get wrong (as indicated by the red writing). Could someone please tell me what I am doing wrong when using the cot(θ) substitution?