Why Are Simple Integrals Split into Two Separate Terms?

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Integrating t sin(at) is preferred over integrating (6 - 3t)sin(at) due to its simplicity. The process of integration by parts is necessary for both integrals, but a simpler integrand streamlines the calculations. This approach reduces complexity and makes the integration process more manageable. Understanding the rationale behind splitting integrals can enhance problem-solving efficiency in calculus. Simplifying integrals into two terms is a strategic choice to facilitate easier calculations.
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Ry122 said:
Could someone please explain to me why this is split into two separate terms?

http://img689.imageshack.us/img689/3092/unledwyx.png
Because it's quite a bit simpler to integrate t sin(at) than to integrate (6 - 3t)sin(at). In both cases you need to use integration by parts, but the simpler integrand makes the process easier.
 
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