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Problem 50 Hard Difficulty

Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take $ C = 0 $).

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

Answer

$\int \tan ^{2} \theta \sec ^{2} \theta d \theta=\frac{\tan ^{3} \theta}{3}+C$

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Video Transcript

given the fact that are you is tan of data. This means that d u over D thing that's the same thing is do you over dx except for instead of X. They've got data on this context is seeking square data. Therefore, we know that d you just written in terms of do you a secret scrub data d theta. Now we have the integral of you scored. Do you? We can integrate this to BU cubed over three years in the power rule, increased export by one divide by the new exponents And now back substituting end we end up with are integral now chek of our answers Reasonable weaken graph and you can see over here this is a reasonable answer.