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Evaluate the integral.
$ \displaystyle \int x \cos 5x dx $
$\int x \cos 5 x d x=\frac{1}{5} x \sin 5 x-\int \frac{1}{5} \sin 5 x d x=\frac{1}{5} x \sin 5 x+\frac{1}{25} \cos 5 x+C$
Calculus 2 / BC
Chapter 7
Techniques of Integration
Section 1
Integration by Parts
Integration Techniques
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Um okay, so we're trying to evaluate the integral of X coast on five x t x. This is a classic, um, integration by parts where he's put you d vehicles, UV minus. V. Do, um you want to carefully choose your you in peace so that you can differentiate you and get rid of it? In a sense. Andi, you have V and you, Khun, still integrate the for the Devi s o you have u equals X and Devi equals Cassandra five x the x and then you find the vehicle's dx the equals one fifth sign of five x Put it all together. Interval of ex co sign of five x t x is equal to one fifth x sign of five X minus one fifth integral of sign of five x t x Notice that I put the one fifth outside of the integral of sine of five x t x because it's a constant, Um, and then you can integrate Sign of five x t x so you get in the end one fifth ex sine x five x plus one over twenty five co sign of five x plus C
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