Question Number 95563 by peter frank last updated on 26/May/20 $$\int\frac{\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}}{\left(\mathrm{x}−\mathrm{p}\right)\left(\mathrm{x}−\mathrm{q}\right)\left(\mathrm{x}−\mathrm{r}\right)}\mathrm{dx} \\ $$ Answered by MJS last updated on 26/May/20 $$\int\frac{{ax}^{\mathrm{2}} +{bx}+{c}}{\left({x}−{p}\right)\left({x}−{q}\right)\left({x}−{r}\right)}{dx}= \\ $$$$=\frac{{ap}^{\mathrm{2}}…
Question Number 161089 by mnjuly1970 last updated on 12/Dec/21 $$ \\ $$$$\:\:{prove}\:{that} \\ $$$$\:\:\:\mathrm{I}=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \mathrm{ln}\:\left(\:\mathrm{1}+\:{sin}\:\left(\mathrm{2}\:\alpha\:\right)\right)\:{d}\alpha\: \\ $$$$\:\:\:\:\:\:\:\:\:\:=\:\:\mathrm{2G}\:−\:\pi\:\mathrm{ln}\:\left(\sqrt{\mathrm{2}}\:\right) \\ $$$$\:\:\:\:\:\:\:\mathrm{G}:\:\:{catalan}\:{constant} \\ $$ Answered by Ar…
Question Number 95549 by Fikret last updated on 25/May/20 $$\int_{−\pi} ^{\pi} \mid{cos}^{\mathrm{3}} {x}\mid{dx} \\ $$ Answered by MJS last updated on 26/May/20 $$\underset{−\pi} {\overset{\pi} {\int}}\mid\mathrm{cos}^{\mathrm{3}}…
Question Number 95548 by hovero clinton last updated on 25/May/20 Commented by hovero clinton last updated on 25/May/20 help solve please Commented by MJS last updated on…
Question Number 95547 by Fikret last updated on 25/May/20 $$\int\frac{\mathrm{2}{x}^{\mathrm{3}} {dx}}{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{3}}=? \\ $$ Answered by MJS last updated on 25/May/20 $$\int\frac{\mathrm{2}{x}^{\mathrm{3}} }{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{3}}{dx}=\int\left({x}+\mathrm{2}+\frac{\mathrm{5}{x}−\mathrm{6}}{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{3}}\right){dx}=…
Question Number 95546 by Fikret last updated on 25/May/20 $$\int{x}^{\mathrm{2}} \sqrt{{a}^{\mathrm{2}} +{x}^{\mathrm{2}} }{dx}=? \\ $$ Answered by MJS last updated on 25/May/20 $$\int{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{2}} +{a}^{\mathrm{2}}…
Question Number 161076 by mnjuly1970 last updated on 11/Dec/21 $$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\:\left(\mathrm{1}+\:{x}\:\right)}{\left(\mathrm{1}+\:{x}^{\:\mathrm{2}} \right)^{\:\mathrm{2}} }\:{dx}\:=\:? \\ $$$$\:\:\:\:\:−−−−−−−−−−−− \\ $$$$\:\:\:\:\:\:\:\: \\ $$ Answered…
Question Number 30008 by Jmasanja last updated on 14/Feb/18 $${integrate}\:{w}.{r}.{t}\:{x} \\ $$$$\int\left({e}^{{x}^{\mathrm{2}} } \right){dx} \\ $$ Commented by abdo imad last updated on 14/Feb/18 $${we}\:{have}\:{e}^{{u}}…
Question Number 95518 by Mikael_786 last updated on 25/May/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 29980 by abdo imad last updated on 14/Feb/18 $${prove}\:{that}\:\gamma=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\left(\frac{\mathrm{1}}{{n}}\:\:−{ln}\left(\mathrm{1}\:+\frac{\mathrm{1}}{{n}}\right)\right) \\ $$$$\left.\mathrm{2}\right){show}\:{that}\:\gamma=\:\sum_{{k}=\mathrm{2}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}}\:\xi\left({k}\right). \\ $$ Terms of Service Privacy Policy…