Question Number 206490 by Simurdiera last updated on 16/Apr/24
$${Resuelve}\:{la}\:{siguiente}\:{integral} \\ $$$$\int\:\frac{\mathrm{cos}\:\left({t}\right)}{\:\sqrt[{\mathrm{4}}]{\mathrm{sin}^{\mathrm{7}} \left({t}\right)\centerdot\mathrm{cos}^{\mathrm{5}} \left({t}\right)}}\:{dt} \\ $$
Answered by Frix last updated on 16/Apr/24
$${t}=\mathrm{tan}\:{x} \\ $$$$\Rightarrow \\ $$$$\int{t}^{−\frac{\mathrm{7}}{\mathrm{4}}} {dt}=−\frac{\mathrm{4}}{\mathrm{3}}{t}^{−\frac{\mathrm{3}}{\mathrm{4}}} =−\frac{\mathrm{4}}{\mathrm{3}\sqrt[{\mathrm{4}}]{\mathrm{tan}^{\mathrm{3}} \:{x}}}+{C} \\ $$