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Numerade Educator

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Problem 38 Medium Difficulty

Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent.

$ \displaystyle \int \csc^5 x\ dx $

Answer

$-\frac{1}{4} \cot x \csc ^{3} x-\frac{3}{8} \cot x \csc x+\frac{3}{8} \ln |\csc x-\cot x|+C$

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Video Transcript

Okay, So this question wants us to find this anti derivative using the computer algebra system and then comparing that with the table answer and showing that they're the same. So using a computer algebra system, I was given this, but we're using a table. I was given this. So let's try and turn this computer algebra system form into the tabular form by expanding everything out. So let's start by distributing and expanded. So we get a 3/8 Ellen Kosi can X minus co Tangin X minus 2/8 Cosi can't squared x Co Seek an axe Co Tanja Necks minus three over eight Kosi can ex co Tanja necks. So now we can do one final simplification on our middle term here by combining our like powers in reducing our fraction. And let's compare this to our table for him. So we need 3/8 Ellen of the difference, which we have. Then we need negative 1/4 Coast. He can't cubed co tangent, and then we did a negative 3/8. Cozy can't go changing, which we have. So the answers are indeed equivalent