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Question Number 183243 by cortano1 last updated on 24/Dec/22

$$\int \frac{\sqrt{\sin x}-\sqrt{\cos x}}{\sqrt{\sin x}+\sqrt{\cos x}}dx=?$$

Answered by MJS_new last updated on 24/Dec/22

$$\int \frac{\sqrt{\sin x}-\sqrt{\cos x}}{\sqrt{\sin x}+\sqrt{\cos x}}dx=$$$$[t=\sqrt{\tan x}\to dx=\frac{2t}{t^4+1}dt]$$$$=2\int \frac{t(t-1)}{(t+1)(t^2-\sqrt{2}t+1)(t^2+\sqrt{2}t+1)}dt$$$$\mathrm{now}\mathrm{decompose}\mathrm{and}\mathrm{solve}$$

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