Question Number 136942 by Mathspace last updated on 28/Mar/21 $${calculate}\:\int_{−\infty} ^{\infty} \:\:\frac{{x}^{\mathrm{2}} {dx}}{\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{5}\right)^{\mathrm{3}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 136943 by Mathspace last updated on 28/Mar/21 $${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{ax}} \mid{sin}\left({bx}\right)\mid\:{dx} \\ $$$${a}>\mathrm{0}\:{and}\:{b}>\mathrm{0} \\ $$ Answered by mathmax by abdo last updated on…
Question Number 136935 by metamorfose last updated on 27/Mar/21 $$\int{cos}\left({x}\right){e}^{{cos}\left({x}\right)+{sin}\left({x}\right)} {dx}=…? \\ $$ Answered by liberty last updated on 27/Mar/21 $$\int\:\mathrm{cos}\:\mathrm{x}.\mathrm{e}^{\mathrm{cos}\:\mathrm{x}} .\mathrm{e}^{\mathrm{sin}\:\mathrm{x}} \:\mathrm{dx}\:= \\ $$$$\mathrm{by}\:\mathrm{parts}…
Question Number 136929 by liberty last updated on 27/Mar/21 $$\int\:\frac{\mathrm{e}^{\mathrm{ln}\:\left(\mathrm{sin}^{−\mathrm{1}} \mathrm{x}\right)} }{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:=\:?\: \\ $$ Answered by Dwaipayan Shikari last updated on 27/Mar/21 $$\int\frac{{e}^{{log}\left({sin}^{−\mathrm{1}} {x}\right)}…
Question Number 136921 by mnjuly1970 last updated on 27/Mar/21 $$\:\:\:\:\:{evaluation}\:{of}\:::\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{xln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$\:\:{solution}: \\ $$$$\:\:\:\:\boldsymbol{\phi}\overset{{I}.{B}.{P}\:} {=}\left[\frac{\mathrm{1}}{\mathrm{2}}{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right){ln}\left(\mathrm{1}+{x}\right)\right]_{\mathrm{0}} ^{\mathrm{1}} −\frac{\mathrm{1}}{\mathrm{2}}\left\{\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}}{dx}=\boldsymbol{\Phi}\right\} \\…
Question Number 136922 by malwan last updated on 27/Mar/21 $$\int\:{ln}\mid{tan}^{−\mathrm{1}} {x}\mid\:{dx}\:=\:? \\ $$ Answered by Olaf last updated on 27/Mar/21 $$\mathrm{F}\left({x}\right)\:=\:\int\mathrm{ln}\mid\mathrm{atan}{x}\mid\:{dx} \\ $$$$\mathrm{Let}\:{u}\:=\:\mathrm{atan}{x} \\ $$$$\mathrm{F}\left({u}\right)\:=\:\int\mathrm{ln}\mid{u}\mid\left(\mathrm{1}+\mathrm{tan}^{\mathrm{2}}…
Question Number 5838 by gourav~ last updated on 31/May/16 $$\int\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cot}\:{x}}{dx} \\ $$ Commented by Yozzii last updated on 31/May/16 $$\frac{\mathrm{1}}{\mathrm{1}+{cotx}}=\frac{{sinx}}{{cosx}+{sinx}} \\ $$$${Let}\:{t}={tan}\mathrm{0}.\mathrm{5}{x}\Rightarrow{dt}=\mathrm{0}.\mathrm{5}{sec}^{\mathrm{2}} \mathrm{0}.\mathrm{5}{dx} \\ $$$${dx}=\frac{\mathrm{2}}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 136905 by leena12345 last updated on 27/Mar/21 $$\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\frac{\mathrm{56}}{{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{5}}{dx} \\ $$ Answered by Mathspace last updated on 27/Mar/21 $$\Psi=\int_{\mathrm{0}} ^{\mathrm{3}} \:\frac{\mathrm{56}}{{x}^{\mathrm{2}}…
Question Number 5835 by sanusihammed last updated on 31/May/16 $${Evaluate}\:{the}\:{integral}. \\ $$$$ \\ $$$$\int\left[\left({x}−\frac{{x}^{\mathrm{3}} }{\mathrm{2}}+\frac{{x}^{\mathrm{5}} }{\mathrm{2}.\mathrm{4}}−\frac{{x}^{\mathrm{7}} }{\mathrm{2}.\mathrm{4}.\mathrm{6}}+…\right)\left(\mathrm{1}−\frac{{x}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} }+\frac{{x}^{\mathrm{4}} }{\mathrm{2}^{\mathrm{2}} .\mathrm{4}^{\mathrm{2}} }−\frac{{x}^{\mathrm{6}} }{\mathrm{2}^{\mathrm{2}} .\mathrm{4}^{\mathrm{2}} .\mathrm{6}^{\mathrm{2}}…
Question Number 136906 by leena12345 last updated on 27/Mar/21 $$\underset{\mathrm{9}} {\overset{\infty} {\int}}\frac{\mathrm{1}}{\left({x}−\mathrm{8}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} }{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 27/Mar/21 $$=−\mathrm{2}\left[\left({x}−\mathrm{8}\right)^{−\frac{\mathrm{1}}{\mathrm{2}}} \right]_{\mathrm{9}}…