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Author: Tinku Tara

evaluation-of-0-1-xln-1-x-1-x-2-dx-solution-I-B-P-1-2-ln-1-x-2-ln-1-x-0-1-1-2-0-1-ln-1-x-2-1-x-dx-1-2-ln-2-2-1-2-

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\} \\…

Solve-simultaneously-2x-y-z-8-i-x-2-y-2-2z-2-14-ii-3x-3-4y-3-z-3-195-iii-Please-help-Thanks-

Question Number 5851 by sanusihammed last updated on 01/Jun/16 $${Solve}\:{simultaneously} \\ $$$$ \\ $$$$\mathrm{2}{x}\:+\:{y}\:−\:{z}\:=\:\mathrm{8}\:\:\:\:………\:\left({i}\right) \\ $$$${x}^{\mathrm{2}} \:−\:{y}^{\mathrm{2}} \:+\:\mathrm{2}{z}^{\mathrm{2}} \:=\:\mathrm{14}\:\:\:\:………\:\left({ii}\right) \\ $$$$\mathrm{3}{x}^{\mathrm{3}} \:+\:\mathrm{4}{y}^{\mathrm{3}} \:+\:{z}^{\mathrm{3}} \:=\:\mathrm{195}\:\:\:\:………..\:\left({iii}\right) \\…

ln-tan-1-x-dx-

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}}…

1-1-cot-x-dx-

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}}…

0-3-56-x-2-6x-5-dx-

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}}…

Evaluate-the-integral-x-x-3-2-x-5-2-4-x-7-2-4-6-1-x-2-2-2-x-4-2-2-4-2-x-6-2-2-4-2-6-2-dx-for-0-lt-x-lt-Please-help-

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-71371

Question Number 71371 by rajesh4661kumar@gmail.com last updated on 14/Oct/19 Commented by prakash jain last updated on 15/Oct/19 $${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{2}{y}−\mathrm{23}=\mathrm{0} \\ $$$$\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\left({y}+\mathrm{1}\right)^{\mathrm{2}} =\mathrm{25} \\…