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# Evaluate the integral.$\displaystyle \int e^{-\theta} \cos 2 \theta d \theta$

## $\int e^{-\theta} \cos 2 \theta d \theta=\frac{1}{5} e^{-\theta}(2 \sin 2 \theta-\cos 2 \theta)+C$

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Integration Techniques

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### Video Transcript

The problem is, you volunteer the integral into next to Theatre Tam's consigned to theta theta. But this problem we were used. My third of the integration by parts. The farmer is integral off you times away from the axe. It's the control. New temps. We minus the integral of your prom times bring Jax. But this problem, like a lot of you, is you go to you two make you later on tonight. Way. Promise he caught you sign to data, then you promise he go too negative. You know, on the way years he called too. Well, have you, um, sign two times data. Now, this integral is we call to you Tom Sweet. So this is one half you two next to you. Sign to data miners and to go off you prom times be So this is class half into your off to next sign to say that you know now localities into grow. So this is same lovers this month, Every kind also use into grow integration. My parts like you is culturing to make you think We promise you go to sign two times in a row. Then you promise the connective it's next leader. And the really difficult to connect. Your half was signed two times data. Now this is Echo two. Half each sign few times a plus. This is one half. You tamps me. Is this you too? Negative leader. Times negative half assign. Two times minus the integral off you. Prom times mean this is the girl of my half. I'm sorry to make you data. We'LL sign who think that No data. This isn't Go to one half. You too, Nate. You data sign. Who damns beta on the minus one. Force you tonight. You are. It was signed to theta on the minus one force and to grow off to connect you. We'LL sign to say that data now located this integral. This is the same as it's integral. So we can move this term. Choose the right left hand side. Then we have one plus one force times and to grow off. It's connective co sign too. Ethan, this is equal to one half. It makes you theatre sign who? Think minus one force you two night you theatre. Assign two hams data. Thanks. This number is five over four, so we multiply full over five for both sides. Then we have integral of connective. I'LL sign to that data. We must fly five a full over five. So this is two over five. It make you leader sign too minus one or five. It makes you did a call sign with Ada on DH class. Asked him number C.

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#### Topics

Integration Techniques

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