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Resuelve-la-siguiente-integral-sin-t-sin-7-t-cos-5-t-1-4-dt-




Question Number 206489 by Simurdiera last updated on 16/Apr/24
Resuelve la siguiente integral  ∫ ((sin (t))/( ((sin^7 (t)∙cos^5 (t)))^(1/4) )) dt
$${Resuelve}\:{la}\:{siguiente}\:{integral} \\ $$$$\int\:\frac{\mathrm{sin}\:\left({t}\right)}{\:\sqrt[{\mathrm{4}}]{\mathrm{sin}^{\mathrm{7}} \left({t}\right)\centerdot\mathrm{cos}^{\mathrm{5}} \left({t}\right)}}\:{dt} \\ $$
Answered by Frix last updated on 16/Apr/24
t=tan x  ⇒  ∫t^(−(3/4)) dt=4t^(1/4) =4((tan x))^(1/4) +C
$${t}=\mathrm{tan}\:{x} \\ $$$$\Rightarrow \\ $$$$\int{t}^{−\frac{\mathrm{3}}{\mathrm{4}}} {dt}=\mathrm{4}{t}^{\frac{\mathrm{1}}{\mathrm{4}}} =\mathrm{4}\sqrt[{\mathrm{4}}]{\mathrm{tan}\:{x}}+{C} \\ $$

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