Question

integrate √tan(x) + √cot(x)​

Answer 1

Answer:

$\sqrt{ \tan(x)} dx + \sqrt{ \cot(x) } dx \\ ( \tan \: x) {}^{ \frac{1}{2} } + ( \cot \: x) {}^{ \frac{1}{2} } \\ \frac{( \tan \: x ) {}^{ \frac{1}{2} + 1} }{ \frac{1}{2} + 1} + \frac{( \cot \: x) {}^{ \frac{1}{2} + 1} }{ \frac{1}{2} + 1 } \\ \frac{2}{3} ( \tan \: x) {}^{ \frac{3}{2} } + \frac{2}{3} ( \cot \: x) {}^{ \frac{3}{2} }$

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