Question

When Integrating by Parts multiple times, do you carry the negative in front of the integral in the forumla uv-(integral)vdu?

Answer 1

I was asked to integrate:
\[\int\limits_{}^{}x^2\cos(x)\]
for context

Answer 2

The negative sign has to be multiplied with the resultant integral
\[\large\rm ∫ab'=ab-(∫a'b)\ \]

Answer 3

Consult Example 9 on this page http://tutorial.math.lamar.edu/Classes/CalcII/IntegrationByParts.aspx

They have a very beautiful trick for long integration by part questions

Answer 4

Thats what I thought too

Answer 5

Ah that is a nice trick. Cool the things you can do if you can recognize a pattern in math

Answer 6

Math is indeed beautiful.