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Category: Integration

d-2sin-2-cos-2-

Question Number 102926 by mohammad17 last updated on 11/Jul/20 $$\:\int\:\frac{{d}\theta}{\mathrm{2}{sin}^{\mathrm{2}} \theta−{cos}^{\mathrm{2}} \theta}\:\:? \\ $$ Answered by OlafThorendsen last updated on 11/Jul/20 $$\int\frac{{d}\theta}{\mathrm{2}\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }−\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }}…

dx-x-3-3x-5-

Question Number 102922 by mohammad17 last updated on 11/Jul/20 $$\int\:\frac{{dx}}{{x}^{\mathrm{3}} +\mathrm{3}{x}−\mathrm{5}}\:\:? \\ $$ Commented by prakash jain last updated on 11/Jul/20 $$\mathrm{The}\:\mathrm{approach}\:\mathrm{you}\:\mathrm{take}\:\mathrm{to}\:\mathrm{solve} \\ $$$$\mathrm{the}\:\mathrm{question} \\…

Question-168459

Question Number 168459 by BegamovSirojiddin last updated on 11/Apr/22 Answered by Mathspace last updated on 11/Apr/22 $${I}=\int\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\frac{\mathrm{5}}{\mathrm{2}}} } \\ $$$${I}=\int\:\:\frac{{dx}}{\left(\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} +\frac{\mathrm{3}}{\mathrm{4}}\right)^{\frac{\mathrm{5}}{\mathrm{2}}} }\:\:\left({x}+\frac{\mathrm{1}}{\mathrm{2}}=\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{tant}\right. \\ $$$${I}=\int\frac{\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\left(\mathrm{1}+{tan}^{\mathrm{2}}…

sin-x-x-dx-

Question Number 102911 by I want to learn more last updated on 11/Jul/20 $$\int\:\frac{\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{x}}\:\:\mathrm{dx} \\ $$ Commented by prakash jain last updated on 11/Jul/20 $$\mathrm{This}\:\mathrm{question}\:\mathrm{has}\:\mathrm{been}\:\mathrm{asked}\:\mathrm{so}\:\mathrm{many}…

Question-168446

Question Number 168446 by amin96 last updated on 10/Apr/22 Answered by Mathspace last updated on 11/Apr/22 $$\Psi=\frac{\mathrm{1}}{\mathrm{2}}\int_{−\infty} ^{+\infty} \:\frac{{cos}\left({nx}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$$$={Re}\left(\frac{\mathrm{1}}{\mathrm{2}}\int_{−\infty} ^{+\infty\:} \frac{{e}^{{inx}} }{{x}^{\mathrm{2}}…