- #1

- 807

- 8

## Homework Statement

The integral of 5/(x^2 + 1) dx from -1 to 1. (The TheIntegral.jpg attachment shows this in a aesthetically-pleasing way.)

## Homework 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)

## 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?