dx-sin2x-sec-x-

Question Number 68116 by aliesam last updated on 05/Sep/19

$$\int \frac{dx}{sin2x-sec\left(x\right)}$$

Commented by MJS last updated on 06/Sep/19

$$\mathrm{look}\mathrm{at}\mathrm{question}68141$$

Answered by MJS last updated on 05/Sep/19

$$\int \frac{dx}{\sin 2x-\sec x}=$$$$[t=\sin x\to dt=\frac{dt}{\cos x}]$$$$=-\frac{1}{2}\int \frac{dt}{t^3-t+\frac{1}{2}}=-\frac{1}{2}\int \frac{dt}{(t-\alpha )(t-\beta )(t+\gamma )}$$$$\mathrm{now}\mathrm{decompose}\mathrm{and}\mathrm{integrate}$$$$\mathrm{at}\mathrm{the}\mathrm{end}\mathrm{solve}{t}^3-t+\frac{1}{2}=0\mathrm{to}\mathrm{get}\mathrm{the}$$$$\mathrm{constant}\mathrm{factors}$$

Commented by mind is power last updated on 05/Sep/19

$$cardan$$$$$$

Commented by MJS last updated on 05/Sep/19

$$\mathrm{what}\mathrm{does}“{\mathrm{cardan}}^{″}\mathrm{mean}?$$

Commented by mind is power last updated on 05/Sep/19

$$cardanisonewaytosolvealgebricequationofdegre3sorryfirmyenglish$$$$$$

Commented by MJS last updated on 06/Sep/19

$$\mathrm{of}\mathrm{course}!\mathrm{you}\mathrm{mean}{\mathrm{Cardano}}^{\prime }\mathrm{s}\mathrm{method},\mathrm{you}$$$$\mathrm{are}\mathrm{right}.\mathrm{I}\mathrm{read}“{\mathrm{cardan}}^{″}\mathrm{and}\mathrm{the}\mathrm{only}\mathrm{thing}$$$$\mathrm{that}\mathrm{came}\mathrm{to}\mathrm{my}\mathrm{mind}\mathrm{was}\mathrm{the}“\mathrm{cardan}\mathrm{shaft}$$$${\mathrm{drive}}^{″}\dots \mathrm{haha},\mathrm{blame}\mathrm{it}\mathrm{on}\mathrm{me}\dots$$

Commented by mind is power last updated on 05/Sep/19

$$yeahsorryimfrenchmyenglishisnotverrygood$$

Commented by MJS last updated on 06/Sep/19

no problem, I'm from Austria... I had 4 years of French in school but that had been 30 years ago... Je peux encore comprendre partiellement le français écrit, mais je ne comprends plus la langue parlée ...

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