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Question Number 126502 by benjo_mathlover last updated on 21/Dec/20

$$\int \frac{dx}{\sqrt{\sin {}^{5}x\cos {}^{7}x}}?$$

Answered by MJS_new last updated on 21/Dec/20

$$\int \frac{dx}{\sqrt{{\sin }^{5}x{\cos }^{7}x}}=$$$$[t=\sqrt{\tan x}\to dx={2\cos }^{2}x\sqrt{\tan x}dt]$$$$=2\int \frac{{(t^4+1)}^2}{t^4}dt=\int (2t^4+4+\frac{2}{t^4})dt=$$$$=\frac{2}{5}{t}^5+4t-\frac{2}{3t^3}=...$$

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