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Numerade Educator



Problem 41 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int \theta \tan^2 \theta\ d \theta $


$\int \theta \tan ^{2} \theta d \theta=\theta \tan \theta-\ln |\sec \theta|-\frac{1}{2} \theta^{2}+c$


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Video Transcript

let's use by parts here. Neuticles Data, D'Oh and then for Devi. So then, from here, we need to integrate chance. Where's so Use one of the Pythagorean identities to rewrite this. And then we have cantina minus data. So recall the formula for parts U V minus integral B to you. So let's plug in our U and V and then minus in a girl. And that here we have tan theta minus Dana and then data and will simplify that in a roll of ten. That's natural. Log absolute value. See, Cam. And then here you have a double minus so that'LL be plus and then finally just combine this with this and that's our answer.