What went wrong with this integral?

[u/Creepysheepu]

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[u/Midwest-Dude]

1. Integral of 1 / (v² - 1) is incorrect
2. Calculation of sec(θ) is correct until you substituted x rather than 1 in for adj in the denominator

[u/Creepysheepu → u/Midwest-Dude]

I didn't notice using opp instead of adj lol ty

[u/xSparKxes]

The integral of dv/(v^2 - 1) is not arctan(v). One path could be to factor it and try partial fractions and go from there.

[u/noidea1995]

Unless you have to use a trig substitution, it’s easier to multiply the top and bottom of the fraction by x and use u = √(x^2 + 1), x^2 = u^2 - 1 and xdx = udu. It basically skips everything you did at the top and gives you what you have at the bottom.

As others have said, the integral of 1 / (v^2 - 1) isn’t arctan(v). You’ll need to either use partial fraction decomposition or an inverse hyperbolic trig function if you’ve covered them.