202211040951 Solution to 2008-CE-AMATH-II-1

Find $\displaystyle{\int (8x+5)^{250}\,\mathrm{d}x}$ .

Roughwork.

$\begin{aligned} &\quad\, \int (8x+5)^{250}\,\mathrm{d}x \\ \dots\enspace &\textrm{let }u=8x+5\textrm{ s.t. }\mathrm{d}x=\frac{\mathrm{d}u}{8}\enspace\dots \\ & = \int u^{250}\,\bigg(\frac{\mathrm{d}u}{8}\bigg) \\ & = \frac{1}{8}\bigg(\frac{u^{251}}{251}\bigg) +C\textrm{ for some constant} \\ & = \frac{(8x+5)^{251}}{2008}+C \\ \end{aligned}$

物理後生﹑掣數學之肘.
小子算數﹑指物理之月.

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