tich phan 12

N

niemkieuloveahbu

[TEX]\blue \mathbf \int \frac{dx}{x^4+1}=\frac{1}{2}\int\frac{(x^2+1)-(x^2-1)}{x^4+1}dx\\ =\frac{1}{2}(\int\frac{x^2+1}{x^4+1}dx-\int\frac{x^2-1}{x^4+1}dx)=\frac{1}{2}[\int\frac{d(x-\frac{1}{x})}{(x-\frac{1}{x})^2+(\sqrt{2})^2}-\int\frac{d(x+\frac{1}{x})}{(x+\frac{1}{x})^2-(\sqrt{2})^2}]\\ =\frac{1}{2}(\frac{1}{\sqrt{2}}arctan {\frac{x^2-1}{x\sqrt{2}}-\frac{1}{2\sqrt{2}}\ln|\frac{x^2-x\sqrt{2}+1}{x^2+x\sqrt{2}+1}|)[/TEX]
 
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