Question Number 85793 by M±th+et£s last updated on 24/Mar/20 $$\int_{\mathrm{1}} ^{\mathrm{2}} \frac{{tan}^{−\mathrm{1}} \left({x}−\mathrm{1}\right)\:{ln}\left({x}−\mathrm{1}\right)}{{x}}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 20257 by tammi last updated on 24/Aug/17 $$\int\frac{{dx}}{\left(\mathrm{1}−{x}\right)\sqrt{\mathrm{1}+{x}}} \\ $$ Answered by Tinkutara last updated on 24/Aug/17 $${t}^{\mathrm{2}} \:=\:{x}\:+\:\mathrm{1} \\ $$$${dx}\:=\:\mathrm{2}{tdt} \\ $$$$\int\frac{\mathrm{2}{tdt}}{\left(\mathrm{2}\:−\:{t}^{\mathrm{2}}…
Question Number 20255 by tammi last updated on 24/Aug/17 $$\int\frac{{x}^{\mathrm{3}} {dx}}{\:\sqrt{{x}−\mathrm{1}}} \\ $$ Answered by Tinkutara last updated on 24/Aug/17 $${x}\:−\:\mathrm{1}\:=\:{t}^{\mathrm{2}} \\ $$$${dx}\:=\:\mathrm{2}{tdt} \\ $$$${x}^{\mathrm{3}}…
Question Number 20256 by tammi last updated on 24/Aug/17 $$\int\frac{{dx}}{\left({x}−\mathrm{4}\right)\sqrt{{x}+\mathrm{3}}} \\ $$ Answered by Tinkutara last updated on 24/Aug/17 $${x}\:+\:\mathrm{3}\:=\:{t}^{\mathrm{2}} \\ $$$${dx}\:=\:\mathrm{2}{tdt} \\ $$$${x}\:−\:\mathrm{4}\:=\:{t}^{\mathrm{2}} \:−\:\mathrm{7}…
Question Number 85789 by Rio Michael last updated on 24/Mar/20 $$\int\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}} \:{dx}\:= \\ $$ Answered by sakeefhasan05@gmail.com last updated on 24/Mar/20 $$=\left(\mathrm{ln}\:\mathrm{x}\right)^{\mathrm{2}} .\mathrm{x}\:−\int\mathrm{x}.\mathrm{2}\left(\mathrm{ln}\:\mathrm{x}\right).\frac{\mathrm{1}}{\mathrm{x}}\mathrm{dx} \\ $$$$=\mathrm{x}\left(\mathrm{ln}\:\mathrm{x}\right)^{\mathrm{2}}…
Question Number 20254 by tammi last updated on 24/Aug/17 $$\int\frac{{dx}}{\left({x}−\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}} \\ $$ Answered by $@ty@m last updated on 25/Aug/17 $${Let}\:{x}−\mathrm{1}=\frac{\mathrm{1}}{{t}} \\ $$$$\Rightarrow{dx}=\frac{−\mathrm{1}}{{t}^{\mathrm{2}} }{dt} \\…
Question Number 20244 by tammi last updated on 24/Aug/17 $$\int\frac{{dx}}{\left(\mathrm{2}−{x}\right)\sqrt{{x}}} \\ $$ Answered by ajfour last updated on 24/Aug/17 $${let}\:\sqrt{{x}}={t}\:\:\:\:\Rightarrow\:\:\:{dx}=\mathrm{2}{tdt} \\ $$$$\int\frac{{dx}}{\left(\mathrm{2}−{x}\right)\sqrt{{x}}}=\int\frac{\mathrm{2}{tdt}}{\left(\mathrm{2}−{t}^{\mathrm{2}} \right){t}} \\ $$$$=−\mathrm{2}\int\frac{{dt}}{{t}^{\mathrm{2}}…
Question Number 85781 by Joel578 last updated on 24/Mar/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \:\left(\mathrm{ln}\:\frac{\mathrm{1}}{{x}}\right)^{−\mathrm{3}/\mathrm{2}} \:{dx} \\ $$ Commented by Joel578 last updated on 24/Mar/20 $$\mathrm{If}\:\mathrm{we}\:\mathrm{use}\:{u}\:=\:\mathrm{ln}\:\frac{\mathrm{1}}{{x}},\:\mathrm{the}\:\mathrm{integral}\:\mathrm{will}\:\mathrm{become} \\ $$$$\int_{\mathrm{0}}…
Question Number 20243 by tammi last updated on 24/Aug/17 $$\int\frac{{dx}}{{x}+\sqrt{{x}}} \\ $$ Answered by $@ty@m last updated on 25/Aug/17 $${Here}\:{I}=\int\frac{\frac{\mathrm{1}}{\:\sqrt{{x}}}}{\:\sqrt{{x}}+\mathrm{1}}{dx}\:\left({dividing}\:{N}^{{r}} \:\&\:{D}^{{r}} \:{by}\:\sqrt{{x}}\right) \\ $$$${Let}\:\sqrt{{x}}+\mathrm{1}={t} \\…
Question Number 20242 by tammi last updated on 24/Aug/17 $$\int\frac{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{11}{x}+\mathrm{26}}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{5}}{dx} \\ $$$${integration}\:{by}\:{partial}\:{fraction} \\ $$ Answered by ajfour last updated on 24/Aug/17 $$\frac{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{11}{x}+\mathrm{26}}{{x}^{\mathrm{2}}…