Question Number 141560 by mnjuly1970 last updated on 20/May/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:……..{Nice}\:….{Calculus}\left({I}\right)…… \\ $$$$\:\:\:\:\:{Evaluate}::\:\: \\ $$$$\:\:\:\:\:\mathrm{I}:=\int_{\mathrm{0}} ^{\:{ln}\left(\mathrm{2}\right)} \frac{{x}}{{e}^{{x}} +\mathrm{2}{e}^{−{x}} −\mathrm{2}}{dx}=? \\ $$$$\:\:\:\:…… \\ $$ Answered…
Question Number 76014 by Master last updated on 22/Dec/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 76015 by Master last updated on 22/Dec/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 10469 by FilupSmith last updated on 11/Feb/17 $$\mathrm{One}\:\mathrm{definition}\:\mathrm{of}\:\:\Gamma\left({x}+\mathrm{1}\right)\:\:\mathrm{is}: \\ $$$$\Gamma\left({x}+\mathrm{1}\right)=\int_{\mathrm{0}} ^{\:\infty} {e}^{−{t}} {t}^{{x}} {dx} \\ $$$$\: \\ $$$$\mathrm{According}\:\mathrm{to}\:\mathrm{WolframAlpha},\:\mathrm{another} \\ $$$$\mathrm{definition}\:\mathrm{is}: \\ $$$$\Gamma\left({x}+\mathrm{1}\right)=\frac{\mathrm{1}}{{e}^{\mathrm{2}{i}\pi{x}} −\mathrm{1}}\oint_{{L}}…
Question Number 141533 by sarkor last updated on 20/May/21 Answered by qaz last updated on 20/May/21 $$\int\frac{{dx}}{\mathrm{1}+\mathrm{3cos}\:^{\mathrm{2}} {x}}=\int\frac{\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{cos}\:^{\mathrm{2}} {x}}{\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{4cos}\:^{\mathrm{2}} {x}}{dx} \\ $$$$=\int\frac{\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{1}}{\mathrm{tan}\:^{\mathrm{2}}…
Question Number 141532 by sarkor last updated on 20/May/21 Answered by qaz last updated on 20/May/21 $$\int\frac{\mathrm{3sin}\:{x}−\mathrm{2cos}\:{x}}{\mathrm{1}+\mathrm{cos}\:{x}}{dx} \\ $$$$=\int\frac{\mathrm{6sin}\:\frac{{x}}{\mathrm{2}}\mathrm{cos}\:\frac{{x}}{\mathrm{2}}−\mathrm{4cos}\:^{\mathrm{2}} \frac{{x}}{\mathrm{2}}+\mathrm{2}}{\mathrm{2cos}\:^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{dx} \\ $$$$=\int\left(\mathrm{3tan}\:\frac{{x}}{\mathrm{2}}−\mathrm{2}+\mathrm{sec}\:^{\mathrm{2}} \frac{{x}}{\mathrm{2}}\right){dx} \\…
Question Number 141529 by sarkor last updated on 20/May/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 141534 by sarkor last updated on 20/May/21 Answered by som(math1967) last updated on 20/May/21 $$\int\boldsymbol{{cos}}^{\mathrm{2}} \boldsymbol{{xsin}}^{\mathrm{8}} \boldsymbol{{xcosxdx}} \\ $$$$=\int\left(\mathrm{1}−\boldsymbol{{sin}}^{\mathrm{2}} \boldsymbol{{x}}\right)\boldsymbol{{sin}}^{\mathrm{8}} \boldsymbol{{xd}}\left(\boldsymbol{{sinx}}\right) \\ $$$$=\int\boldsymbol{{sin}}^{\mathrm{8}}…
Question Number 141528 by sarkor last updated on 20/May/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 141530 by sarkor last updated on 20/May/21 Commented by mohammad17 last updated on 20/May/21 $$=\int\:\frac{{x}^{\mathrm{2}} −\mathrm{9}+\mathrm{9}}{\:\sqrt{{x}−\mathrm{3}}}{dx}=\int\:\frac{\left({x}−\mathrm{3}\right)\left({x}+\mathrm{3}\right)}{\:\sqrt{{x}−\mathrm{3}}}{dx}+\int\:\frac{\mathrm{9}}{\:\sqrt{{x}−\mathrm{3}}}{dx} \\ $$$$ \\ $$$$=\int\left(\sqrt{{x}−\mathrm{3}}\right)\left({x}+\mathrm{3}\right){dx}+\int\mathrm{9}\left({x}−\mathrm{3}\right)^{−\frac{\mathrm{1}}{\mathrm{2}}} {dx} \\ $$$$…