Question: Evaluate the following integrals:

1. \(\int{\left( {{x}^{3}}+\sqrt{x} \right)dx}\)
2. \(\int{\left( \frac{{{x}^{4}}-2{{x}^{3}}+1}{{{x}^{2}}} \right)}dx\)
3. \(\int\limits_{0}^{4}{\sqrt{x}dx}\)
4. \(\int{{{x}^{2}}{{\left( {{x}^{3}}+5 \right)}^{9}}dx}\)
5. \(\int{\left( x+2 \right)}\left( {{x}^{2}}+4x+1 \right)\)

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