Question Number 95586 by turbo msup by abdo last updated on 26/May/20 $${find}\:\int\:\:\frac{{dx}}{{x}^{{n}} \left({x}+\mathrm{1}\right)^{{m}} }\:\: \\ $$$${m}\:{and}\:{n}\:{integr} \\ $$ Commented by Tony Lin last updated…
Question Number 95584 by turbo msup by abdo last updated on 26/May/20 $${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{dx}}{{x}^{\mathrm{3}} \left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{4}} } \\ $$$$\left.\mathrm{1}\right){without}\:{use}\:{of}\:{decomposition} \\ $$$$\left.\mathrm{2}\right){by}\:{use}\:{of}\:{decomposition} \\ $$ Answered by…
Question Number 95585 by turbo msup by abdo last updated on 26/May/20 $${calculate}\:\int_{\mathrm{2}} ^{+\infty} \:\:\:\frac{{dx}}{\left({x}−\mathrm{1}\right)^{\mathrm{4}} \left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$ \\ $$ Answered by MJS…
Question Number 95581 by Ar Brandon last updated on 26/May/20 $$\int\mathrm{ln}\mid\mathrm{cot}\left(\mathrm{x}/\mathrm{2}\right)\mid\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 161100 by bobhans last updated on 13/Dec/21 $$\mathrm{f}\left(\mathrm{x}^{\mathrm{2}} \right)=\:\mathrm{2}+\int_{\:\mathrm{0}} ^{\:\mathrm{x}^{\mathrm{2}} } \mathrm{f}\left(\mathrm{y}\right)\:\left(\mathrm{1}−\mathrm{tan}\:\mathrm{y}\right)\mathrm{dy}\:,\:\forall\mathrm{x}\in\mathbb{R} \\ $$$$\:\mathrm{f}\left(−\pi\right)=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 95562 by peter frank last updated on 26/May/20 $$\mathrm{show}\:\mathrm{that} \\ $$$$\int\frac{\mathrm{sin}\:\left(\mathrm{x}−\theta\right)}{\mathrm{sin}\:\mathrm{x}}\mathrm{dx}=\mathrm{xcos}\:\mathrm{x}−\mathrm{sin}\:\theta\mathrm{log}\:\mathrm{sin}\:\mathrm{x} \\ $$ Answered by Ar Brandon last updated on 26/May/20 $$\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\mathrm{x}}−\boldsymbol{\theta}\right)=\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\theta}\right)−\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\theta}\right) \\…
Question Number 95563 by peter frank last updated on 26/May/20 $$\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…