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