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solve-t-6-t-2-3-2-dt-




Question Number 189345 by Michaelfaraday last updated on 15/Mar/23
solve  ∫t^(−6) (t^2 +3)^2 dt
$${solve} \\ $$$$\int{t}^{−\mathrm{6}} \left({t}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} {dt} \\ $$
Answered by Frix last updated on 15/Mar/23
=∫((1/t^2 )+(6/t^4 )+(9/t^6 ))dt=−(1/t)−(2/t^3 )−(9/(5t^5 ))=−((5t^4 +10t^2 +9)/(5t^5 ))
$$=\int\left(\frac{\mathrm{1}}{{t}^{\mathrm{2}} }+\frac{\mathrm{6}}{{t}^{\mathrm{4}} }+\frac{\mathrm{9}}{{t}^{\mathrm{6}} }\right){dt}=−\frac{\mathrm{1}}{{t}}−\frac{\mathrm{2}}{{t}^{\mathrm{3}} }−\frac{\mathrm{9}}{\mathrm{5}{t}^{\mathrm{5}} }=−\frac{\mathrm{5}{t}^{\mathrm{4}} +\mathrm{10}{t}^{\mathrm{2}} +\mathrm{9}}{\mathrm{5}{t}^{\mathrm{5}} } \\ $$
Commented by Michaelfaraday last updated on 15/Mar/23
thanks sir
$${thanks}\:{sir} \\ $$

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