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Question Number 70808 by rajesh4661kumar@gmail.com last updated on 08/Oct/19

Answered by MJS last updated on 08/Oct/19

$$\int {\left(\sec x\right)}^{\frac{2}{3}}{\left(\csc x\right)}^{\frac{4}{3}}dx=\int \frac{dx}{\sin x\cos x{\left(\tan x\right)}^{\frac{1}{3}}}=$$$$[t=\tan x\to dx={\left(\cos x\right)}^{2}dt]$$$$=\int \frac{dt}{t^{\frac{4}{3}}}=-\frac{3}{t^{\frac{1}{3}}}=-\frac{3}{{\left(\tan x\right)}^{\frac{1}{3}}}+C$$

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