If I wanted to integrate [itex]\int \sqrt{1+x^2} dx[/itex], I would let [itex]x=\tan\theta[/itex] , which implies [itex]dx=\sec^2 \theta dx[/itex] so that I would have:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int \sqrt{1+x^2} dx = \int \sqrt{1 + \tan^2 \theta} \sec \theta d \theta = \int \sqrt{\sec^2 \theta}\sec^2\theta d\theta = \int \sec^3 \theta d \theta[/itex]

It is this last equality that I am questioning. Why is it not [itex]\int |\sec \theta| \sec^2 \theta d \theta[/itex]?

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# Ignoring positive/negative values with trig substitutions?

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