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Question Number 86328 by M±th+et£s last updated on 28/Mar/20

$$\int \frac{x^2-1}{(x^2+1)\sqrt{1+x^4}}dx$$

Answered by TANMAY PANACEA. last updated on 28/Mar/20

$$\int \frac{1-\frac{1}{x^2}}{1+\frac{1}{x^2}\times x\sqrt{x^2+\frac{1}{x^2}}}dx$$$$\int \frac{d(x+\frac{1}{x})}{(x+\frac{1}{x})\sqrt{{(x+\frac{1}{x})}^2-2}}dx$$$$\int \frac{dk}{k\sqrt{k^2-2}}$$$$k=\sqrt{2}sec\theta$$$$\int \frac{\sqrt{2}sec\theta tan\theta d\theta }{\sqrt{2}sec\theta .\sqrt{2}tan\theta }$$$$\frac{1}{\sqrt{2}}\int d\theta =\frac{\theta }{\sqrt{2}}+c$$$$\frac{1}{\sqrt{2}}{sec}^{-1}\left(\frac{k}{\sqrt{2}}\right)+c$$$$\frac{1}{\sqrt{2}}{sec}^{-1}\left(\frac{x+\frac{1}{x}}{\sqrt{2}}\right)+c$$$$$$$$$$

Commented by M±th+et£s last updated on 28/Mar/20

$$godblessyousir$$

Commented by TANMAY PANACEA. last updated on 28/Mar/20

$$nowcovid19cegulfedtheworld...sogodmaybless$$$$tokillthevirus...$$

Commented by niroj last updated on 28/Mar/20

$$\mathrm{Yes}\mathrm{sir},\mathrm{Now}\mathrm{the}\mathrm{time}\mathrm{is}\mathrm{very}\mathrm{creatical}\mathrm{situation}\mathrm{entire}\mathrm{over}\mathrm{world}$$$$\mathrm{So}\mathrm{we}\mathrm{must}\mathrm{prey}\mathrm{our}\mathrm{god}\mathrm{even}\mathrm{each}\mathrm{religion}\mathrm{to}\mathrm{find}\mathrm{early}\mathrm{medicine}\mathrm{from}\mathrm{world}\mathrm{medical}\mathrm{team}.$$$$\mathrm{Then}\mathrm{it}\mathrm{will}\mathrm{be}\mathrm{welfare}\mathrm{for}\mathrm{all}\mathrm{public}\mathrm{health}\mathrm{and}\mathrm{peacefull}\mathrm{life}.$$$$\mathrm{Please}\mathrm{all},\mathrm{dear}\mathrm{sir}\mathrm{follow}\mathrm{the}\mathrm{strickly}\mathrm{dailly}\mathrm{health}\mathrm{protection}\mathrm{for}\mathrm{your}\mathrm{safety}\mathrm{and}$$$$\mathrm{also}\mathrm{follow}\mathrm{the}\mathrm{respectively}\mathrm{lock}\mathrm{down}\mathrm{area}\mathrm{when}\mathrm{government}\mathrm{are}\mathrm{order}\mathrm{in}\mathrm{each}\mathrm{country}\mathrm{whatever}\mathrm{we}\mathrm{are}\mathrm{now}.$$$$\mathrm{Some}\mathrm{days}\mathrm{we}\mathrm{are}\mathrm{suffereing}\mathrm{we}\mathrm{will}\mathrm{not}\mathrm{die}\mathrm{but}\mathrm{if}\mathrm{we}\mathrm{destroy}\mathrm{the}\mathrm{rule}\mathrm{may}\mathrm{be}\mathrm{chances}\mathrm{to}\mathrm{effected}\mathrm{by}\mathrm{virus}.$$$$\mathrm{So}\mathrm{that}\mathrm{be}\mathrm{safety}\mathrm{and}\mathrm{awareness}$$$$\mathrm{all}\mathrm{the}\mathrm{people}\mathrm{from}\mathbf{C}\mathrm{O}\mathbf{VID}-19.$$$$\mathrm{thank}\mathrm{you}.$$$$$$

Commented by peter frank last updated on 29/Mar/20

$$thankyou$$

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