hey how to do integraTion by parts . im too confused

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hey how to do integraTion by parts . im too confused

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[\int\limits_{}^{}udv = uv - \int\limits_{}^{}vdu\]
Do you recall this equation?
int xcos(x) dx

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it doesnt have any limits is it like we have to go with ILATE =integer log arithemtic trigo and then exponential im confused that wich one is suposed to be integrated or differentiated first
Differentiate x and integrate cosx.
Because x will differentiate to 1 and cosx will just alternate between sinx and back and forth.
Of course with chain rule.
x cos(x) dx solution is : int x cos(x) dx = x sin(x)−int sin(x) dx = x sin(x)+cos(x)+c.
Correct.
Anything else?

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