<s>[INST] Constant when integrating I was integrating $(t+2)^2$ by using the substitution method and by expanding the function. By expanding it then integrating I got the same answer as the book ($\frac{1}{3}(t^3+6t^2+12t)+C$), but when I substituted I got $\frac{1}{3}\cdot(t+2)^3 + C = \frac{1}{3} \cdot (t^3+6t^2+12t+8) + C$.
Am I missing something here? Got an 8 at the end when substituting, but no constant when expanding.
 [/INST] No worries,
$$\left(\frac{1}{3}(t^3+6t^2+12t)+C\right)'=t^2+4t+4$$
and
$$\left(\frac{1}{3}(t+2)^3 + C \right)'=(t+2)^2.$$
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