\[\integral\_{}^{}{\text{cos} ⥂ \text{e}\text{c}^{4}x}dx] | MATH - INTEGRATION BY SUBSTITUTION | SolveeIt

$\int_{}^{}{\text{cos} ⥂ \text{e}\text{c}^{4}x}dx$

$\cot x + \frac{\cot^{3}x}{3} + c$

$\tan x + \frac{\tan^{3}x}{3} + c$

$\cot x - \frac{\cot^{3}x}{3} + c$

$- \tan x - \frac{\tan^{3}x}{3} + c$

Answer

$\cot x - \frac{\cot^{3}x}{3} + c$

Explanation

$\int_{}^{}{c\text{os} ⥂ \text{e}\text{c}^{4}x}dx =$

$\int \operatorname { cosec } ^ { 2 } x \left( 1 + \cot ^ { 2 } x \right) d x$

$= - \cot x + \frac{(\cot x)^{3}}{3} + c.$

Question: \[\int_{}^{}{\text{cos} ⥂ \text{e}\text{c}^{4}x}dx\]...