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Numerade Educator

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Problem 15 Easy Difficulty

Find the general indefinite integral.

$ \displaystyle \int (2 + \tan^2 \theta)\, d\theta $

Answer

$$\theta+\tan \theta+C$$

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Video Transcript

uh this problem is actually doable. Um You just need a lot of practice to recognize a pattern like this. And I don't have good advice other than to know your trig identities. Um And the reason why is a I'm gonna rewrite tangent squared with what it's equal to and one of the trig identities I'm talking about is uh Mhm tangent squared of theta Plus one is equal to seek and squared of data. So by doing a little algebra manipulation, I'm going to leave most of this alone. I may replace tangent squared, switch over to read to seek and squared And subtract one over. Uh mentally that in black and you might be sitting there saying why on earth would you do that? Well now we can combine like terms to be one plus second squared of data. D theta And the reason why that's to your benefits when with data being your independent variable, then the anti derivative of one would just be data Because the drift of the state will be one. And I'm thinking about the derivative of something that equal second squared. And that answer is tangent of state is directive is seeking squared, and then you just need to remember to add your constant plus C. You have the correct answer. Mhm.