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SL
Numerade Educator

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Problem 1 Easy Difficulty

Evaluate the integral using integration by parts with the indicated choices of $ u $ and $ dv $.

$ \displaystyle \int xe^{2x} $ ; $ u = x $ , $ dv = e^{2x} dx $

Answer

$$
\frac{1}{2} x e^{2 x}-\frac{1}{4} e^{2 x}
$$

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Video Transcript

Okay, So for this question, we need to evaluate the integral You seeing integration by parts so and with the indicator choice ofthe U N TV. So basically you envy are given we need to solve for you nb andi, you were already know Eco's tow X So let's final was res. So the difference show off me goes to you two The power to x the x a so we can see there's differentiations in front ofthe this b So all we need to do is bring this inside the different show. Um, in other words, you need to find the anti duty of all of this. So which is it that he and degenerative of you to the put poverty? O X is just a one half You two have hard to x. Okay. So as we can see our v very cose to I have need to horror to x What so this we can rewrite the integral buy you a TV and the bad formula off in equation by parts. This is just a movie Miners I mean you. Now we just plug in Are you and me are are u S X his ex times means of have times the power to x to X miners their gracious my half You have power to X or years ex toys DX. Yeah. Okay, so we know that anti duty of this thing is just, um, one forest off you to the power to X. So it's well, deep by half. It copied down the first term, Linus. One quarter to have power to X, and this will be our answer.