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Evaluate the following integrals using integration by parts.$$\int x \cos 5 x \, d x$$

$\dfrac{1}{5}$ x sin 5x + $\dfrac{1}{25}$ cos 5x + C

Calculus 1 / AB

Calculus 2 / BC

Chapter 8

Integration Techniques

Section 2

Integration by Parts

Integrals

Integration

Applications of Integration

Baylor University

University of Michigan - Ann Arbor

Boston College

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So we have X times. Go sign five x bx So we're gonna do this by integrating by parts So I will take excess. You and DVS co signed five x So you is X Ah Devi is co signed five x So do you is one v will be ah signed five x over five So that's signed five x over five. So let's start by doing the following So you Devi two girl a few d v is equal to you ve minus integral of e do you? So we already have the left side So you his ex times signed five x over five minus integral of V which is signed five x over five times. Do you, which is one those will just be signed five x over five so x Times signed five x over five minus 1/5 integral off sign five x So uh, signed five x is minus co signed five x over five So this will be X signed five x over five minus 1/5 times minus co signed five X divided by five So, uh, expanding this we'll get X sign five x over five plus co sign five x over 25. So this is our final and

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