Evaluate
[tex]\int (12t^2\text{ + 7t -5) dt }[/tex]
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Rule
[tex]\int (t^n\text{) dt = }\frac{t^{n+1}}{n+1}[/tex]
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So then,
[tex]\int (t^2\text{) dt = }\frac{t^{2+1}}{2+1}=\frac{1}{3}t^3[/tex]
[tex]\int (t^{}\text{) dt = }\frac{t^{1+1}}{1+1}=\frac{1}{2}t^2[/tex]
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Answer
[tex]\int (12t^2\text{ + 7t -5) dt }=\text{ }\frac{12}{3}t^{3\text{ }}+\frac{7}{2}t^2\text{ - 5 t +c= }4t^{3\text{ }}+\frac{7}{2}t^2\text{ - 5 t +c}[/tex]
