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evaluate [tex] \int \limits^5_2 { x^{2} +3x} \, dx [/tex]

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Konrad509idn
[tex]\int \limits_2^5x^2+3x\, dx=\\ \Big[\frac{x^3}{3}+\frac{3x^2}{2}\Big]_2^5=\\ \frac{5^3}{3}+\frac{3\cdot5^2}{2}-(\frac{2^3}{3}+\frac{3\cdot2^2}{2})=\\ \frac{125}{3}+\frac{75}{2}-(\frac{8}{3}+6)=\\ \frac{250}{6}+\frac{225}{6}-(\frac{16}{6}+\frac{36}{6})=\\ \frac{475}{6}-\frac{52}{6}=\\ \frac{423}{6}=\frac{141}{2}=70.5[/tex]
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