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1-1-x-4-dx-

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Question Number 131 by novrya last updated on 25/Jan/15
∫(1/(1+x^4 )) dx =....
$$\int\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{4}} }\:{dx}\:=…. \\ $$$$ \\ $$
Answered by rajabhay last updated on 08/Dec/14
∫(1/(1+x^4 ))dx=∫(1/2)(((x^2 +1)/(1+x^4 )) −((x^2 −1)/(1+x^4 )))dx See answer to Q119 to see the steps after this point
$$\int\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{4}} }{dx}=\int\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{{x}^{\mathrm{2}} +\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{4}} }\:−\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{4}} }\right){dx} \\ $$$$\boldsymbol{\mathrm{See}}\:\boldsymbol{\mathrm{answer}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{Q}}\mathrm{119}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{see}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{steps}} \\ $$$$\boldsymbol{\mathrm{after}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{point}} \\ $$

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