Find the integral of xcos5x dx

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SUMMARY

The integral of xcos(5x) dx can be solved using integration by parts, specifically the formula uv - ∫v du. The discussion highlights two approaches to selecting u and dv: the book's method of choosing u=x and dv=cos(5x) dx is preferred for simplifying the integrand. The alternative choice of u=cos(5x) and dv=xdx is valid but less effective in this context, as it complicates the integration process.

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Homework Statement


Find the integral of xcos5x dx


Homework Equations


uv- (integral)vdu


The Attempt at a Solution



I tried to pick u=cos5x and dv=xdx, but the book uses u=x, dv=cos5x dx

Why can't my way work?
 
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fk378 said:
Why can't my way work?

It can. Generally, people choose the u and v so that the problem is simplified - the way the book chooses makes the integrand more tractable.
 

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