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JH
Numerade Educator

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Problem 15 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int \cot x \cos^2 x dx $

Answer

$\ln (\sin x)-\frac{\sin ^{2} x}{2}+C$

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Video Transcript

This problem is from Chapter seven section to problem number fifteen in the book Calculus only Transcendental Sze eighth edition by James Tour And here we have an indefinite run Girl off co tension of X Times co sign squared of X. So let's re write it both of these these terms and in a grand so I can rewrite co tension using the definition as co signer bags over sign eggs and for close on square of X, we can rewrite This is one minus science fair legs and that's from using our one of our pathetic man identities. So next we gonna apply U substitution here, let's take you two be signing books so that do you is co sign of X d. X. If we play our U substitution, this integral becomes one minus. You square over you, do you which we can rewrite as you to the minus one minus you, me and we can evaluate each of these inner rules by using the power rule for the integral. So for this first integral, we have the national log absolute value of you minus You squared over two. What? Plus he and our last step would be to just replace you with sign of X from our U substitution. So if we do this, we get the natural log. Absolute value of sine X minus science where X over, too. What? Plus he and there's our answer.