Question Number 83737 by jagoll last updated on 05/Mar/20 $$\int\:\:\frac{{x}^{\mathrm{3}} }{{x}^{\mathrm{4}} +\mathrm{cos}\:{x}}\:{dx}\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 83713 by mhmd last updated on 05/Mar/20 $$\int\frac{{dx}}{\:\sqrt{{x}+\sqrt{{x}+\sqrt{{x}}}}}\:\:\:{pleas}\:{sir}\:{help}\:{me} \\ $$ Commented by niroj last updated on 05/Mar/20 $$ \\ $$$$\:\:\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}}}}}\mathrm{dx} \\ $$$$\:=\:\int\:\frac{\:\:\mathrm{1}}{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{4x}+\mathrm{1}}}{\mathrm{2}}}\mathrm{dx}=\:\int\:\frac{\mathrm{2}}{\mathrm{1}+\sqrt{\mathrm{4x}+\mathrm{1}}}\mathrm{dx} \\…
Question Number 149241 by john_santu last updated on 04/Aug/21 Answered by ajfour last updated on 04/Aug/21 $${s}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{x}^{\mathrm{3}} {dx}}{\left({x}−\mathrm{1}\right)^{\mathrm{3}} +\left(\mathrm{3}−{h}\right)\left({x}−\mathrm{1}\right)+{hx}} \\ $$$$\mathrm{3}−{h}=\mathrm{5}\:\:\:\Rightarrow\:\:{h}=−\mathrm{2} \\ $$$${s}_{\mathrm{1}}…
Question Number 83691 by niroj last updated on 05/Mar/20 $$\:\mathrm{evaluate}: \\ $$$$\:\:\:\int\:\frac{\:\boldsymbol{\mathrm{dx}}}{\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{b}}\:\boldsymbol{\mathrm{cos}}\:\boldsymbol{\mathrm{x}}} \\ $$ Commented by mathmax by abdo last updated on 05/Mar/20 $${we}\:{use}\:{changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:\Rightarrow \\…
Question Number 149205 by ArielVyny last updated on 03/Aug/21 $$\int_{−\infty} ^{\mathrm{0}} \frac{{t}}{\left(\mathrm{1}−{t}\right)^{\mathrm{2}} }{dt} \\ $$ Answered by MJS_new last updated on 03/Aug/21 $$\int\frac{{t}}{\left(\mathrm{1}−{t}\right)^{\mathrm{2}} }{dt}=\int\frac{{dt}}{{t}−\mathrm{1}}+\int\frac{{dt}}{\left({t}−\mathrm{1}\right)^{\mathrm{2}} }=…
Question Number 83675 by niroj last updated on 05/Mar/20 $$ \\ $$$$\: \\ $$$$\:\:\mathrm{evaluate}: \\ $$$$\:\mathrm{2}\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \:\frac{\sqrt{\mathrm{x}+\mathrm{1}}}{\mathrm{x}^{\mathrm{2}} +\mathrm{4}}\mathrm{dx} \\ $$$$\:\:\:\:\: \\ $$$$\:\: \\ $$…
Question Number 83642 by niroj last updated on 04/Mar/20 $$ \\ $$$$\: \\ $$$$\mathfrak{Find}\:\mathfrak{the}\:\mathfrak{surface}\:\mathfrak{area}\:\mathfrak{of}\:\mathfrak{the}\:\mathfrak{solid}\:\mathfrak{generated} \\ $$$$\:\:\mathfrak{by}\:\mathfrak{the}\:\mathfrak{revolution}\:\mathfrak{of}\:\mathfrak{the}\:\mathfrak{cardioids}\:\mathfrak{r}=\mathfrak{a}\left(\mathrm{1}+\mathfrak{cos}\:\theta\right)\:\mathfrak{about}\:\mathfrak{the}\:\mathfrak{initial}\:\mathfrak{line}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 149157 by gsk2684 last updated on 03/Aug/21 $$\underset{\frac{\mathrm{1}}{\mathrm{2}}} {\overset{\mathrm{2}} {\int}}\frac{\mathrm{1}}{{x}}\mathrm{cosec}\:^{\mathrm{101}} \left({x}−\frac{\mathrm{1}}{{x}}\right)\:{dx}=? \\ $$ Answered by Kamel last updated on 03/Aug/21 $$\mathrm{0} \\ $$…
Question Number 149156 by gsk2684 last updated on 03/Aug/21 $${if}\:\int\frac{{dx}}{\:\sqrt[{\mathrm{2012}}]{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{1012}} \left(\mathrm{2}+{x}^{\mathrm{2}} \right)^{\mathrm{3012}} }}=\frac{\alpha}{\mathrm{2}\beta}\left(\mathrm{1}−{f}\left({x}\right)\right)^{\frac{\beta}{\alpha}} \\ $$$${then}\:{find}\:\alpha,\beta,{f}\left({x}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 18066 by tawa tawa last updated on 14/Jul/17 $$\left(\mathrm{a}\right)\:\:\mathrm{Evaluate}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}:\:\:\mathrm{y}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{3x}\:+\:\mathrm{1}}{\mathrm{2x}^{\mathrm{2}} \:−\:\mathrm{2x}\:+\:\mathrm{3}} \\ $$$$\left(\mathrm{b}\right)\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{constant}\:\mathrm{A},\:\mathrm{B},\:\mathrm{C}\:\mathrm{in}\:\mathrm{the}\:\mathrm{identity}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{3x}^{\mathrm{2}} \:−\:\mathrm{ax}}{\left(\mathrm{x}\:−\:\mathrm{2a}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{a}^{\mathrm{2}} \right)}\:\equiv\:\frac{\mathrm{A}}{\left(\mathrm{x}\:−\:\mathrm{2a}\right)}\:+\:\frac{\mathrm{Bx}\:+\:\mathrm{Ca}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{a}^{\mathrm{2}} \right)} \\ $$$$\mathrm{where}\:\:\mathrm{a}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant},\:\:\mathrm{hence}\:\mathrm{prove}\:\mathrm{that}.\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}}…