Question

\[\int\limits_{}^{}\sqrt{\tan(x)}dx\]

Answer 1

u-sub??

Answer 2

what do I u-sub? :D

Answer 3

disclaimer: not my solution

Answer 4

@sillybilly123 I actually don't quite understand some of the steps of this integration could you help explain how to get from sqrt(tanx)+ sqrt(cotanx) to the next steps?

Answer 5

\(\sqrt {\tan (x) } + \sqrt {\cot (x) }\)

\(= \sqrt {\dfrac{\sin x}{\cos x} } + \sqrt {\dfrac{\cos x}{\sin x} }\)

\( =\dfrac{\sin x + \cos x}{\sqrt{\sin x \cos x}}\)

\( =\dfrac{\sin x + \cos x}{\sqrt{\frac{1}{2}\sin 2x }}\)

\( = \sqrt 2 \left( \dfrac{\sin x + \cos x}{\sqrt{ \sin 2x }}\right)\)