Can this be solved in terms of elementary functions? If not, what is the approach?
$\int \sec x \sqrt{\tan x} \,\mathrm{d}x$
$\int \sec x \sqrt{\tan x} \, \mathrm dx$
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integration
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3Please see here: http://www.wolframalpha.com/input/?i=integrate+sec+x+(tan+x)%5E(0.5) – 2017-01-28
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0Why care about this? – 2017-01-28
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0this integral leads to an elliptic function – 2017-01-28
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0No, it cannot be solved in terms of elementary functions. Solving it gives elliptic integrals of the first and second kind. – 2017-01-28
1 Answers
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Let $\sqrt{\tan x}=t$.
Hence, $\frac{dx}{\cos^2x}=2tdt$, which gives $dx=\frac{2tdt}{1+t^4}$.
Hence, we need to calculate the following $\int\frac{2t^2}{\sqrt{1+t^4}}dt$