I'm working this problem:
∫ [1-tan^2 (x)] / [sec^2 (x)] dx
∫(1/secx)-[(sin^2x/cos^2x)/(1/cosx)
∫cosx-sinx(sinx/cosx)
∫cosx-∫sin^2(x)/cosx
sinx-∫(1-cos^2(x))/cosx
sinx-∫(1/cosx)-cosx
sinx-∫secx-∫cosx
sinx-sinx-∫secx
=-ln |secxtanx|+C
Can someone just verify that I did everything correctly?
Yes, your work is correct. You simplified the integral correctly step by step, and your final answer of -ln |sec(x)tan(x)| + C is accurate. Good job!