Question

23. Evaluate: f cot^4 x dx​

Answer 1

Step-by-step explanation:

We have,

$\int \cot^{4} (x) dx$

$= \int \cot^{2} (x) .\cot^{2} (x) dx$

$= \int( \cosec^{2} (x) - 1) .\cot^{2} (x) dx$

$= \int\cosec^{2} (x) .\cot^{2} (x) dx - \int \cot^{2} (x)dx$

Let cot(x) = t => -cosec²(x)dx=dt

$= - \int \: t^{2} dt - \int \cosec^{2} (x)dx + \int \: dx$

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

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