Question Number 81290 by mind is power last updated on 11/Feb/20 $$\int_{−\mathrm{1}} ^{\mathrm{1}} {arctan}\left({x}\right){arctan}\left(\frac{{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\right){arctan}\left(\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\right){dx} \\ $$ Commented by msup trace by abdo last updated…
Question Number 81279 by jagoll last updated on 11/Feb/20 $$\int\:\frac{\sqrt{\mathrm{2}{x}+\mathrm{1}}}{\mathrm{3}{x}}\:{dx}\:=\:? \\ $$ Commented by john santu last updated on 11/Feb/20 $${let}\:{u}^{\mathrm{2}} \:=\:\mathrm{2}{x}+\mathrm{1}\:\Rightarrow{x}\:=\:\frac{{u}^{\mathrm{2}} −\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow\frac{\mathrm{2}}{\mathrm{3}}\int\:\:\frac{{u}.\:{udu}}{{u}^{\mathrm{2}}…
Question Number 146790 by puissant last updated on 15/Jul/21 $$\int\frac{\mathrm{1}}{\mathrm{x}}\:\mathrm{e}^{−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }} \mathrm{dx} \\ $$ Answered by Cyriille last updated on 15/Jul/21 $$\boldsymbol{\mathrm{I}}=\int\frac{\mathrm{1}}{{x}}{e}^{-\frac{\mathrm{1}}{{x}^{\mathrm{2}} }} {dx} \\…
Question Number 146791 by puissant last updated on 15/Jul/21 $$\int\frac{\mathrm{x}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}\right)}\mathrm{dx} \\ $$ Answered by Ar Brandon last updated on 15/Jul/21 $$\mathrm{I}=\int\frac{\mathrm{x}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \mathrm{x}}\mathrm{dx}=\int\frac{\mathrm{xsec}^{\mathrm{2}} \mathrm{x}}{\mathrm{sec}^{\mathrm{2}} \mathrm{x}+\mathrm{1}}\mathrm{dx}…
Question Number 146767 by qaz last updated on 15/Jul/21 $$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}+\mathrm{1}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}+…+\frac{\mathrm{1}}{\mathrm{2n}+\mathrm{1}}\right)=? \\ $$ Answered by mnjuly1970 last updated on 16/Jul/21 $$\:\:=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}}…
Question Number 146756 by Bens last updated on 15/Jul/21 $$ \\ $$$$ \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:{t}^{\mathrm{2}} \:+\:\mathrm{1}\:{dt} \\ $$ Answered by tabata last updated on…
Question Number 146752 by Bens last updated on 15/Jul/21 $$ \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:{t}^{\mathrm{2}} +\:\frac{\mathrm{1}}{\mathrm{2}}{t}\:−\mathrm{6}{dx}\:\: \\ $$ Answered by puissant last updated on 15/Jul/21 $$=\mathrm{t}^{\mathrm{2}}…
Question Number 146736 by mnjuly1970 last updated on 15/Jul/21 $$ \\ $$$$\:\:\:\:\:\:\mathrm{1}:\:\:\:\:\mathrm{S}:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{\:{n}−\mathrm{1}} }{{n}.\mathrm{2}^{\:{n}} }\:=? \\ $$$$\:\:\:\:\:\:\mathrm{2}:\:\:\:\:\mathrm{A}:=\:\Sigma\frac{\left(−\mathrm{1}\right)^{\:{n}−\mathrm{1}} }{{n}^{\mathrm{2}} .\:\mathrm{2}^{\:{n}} }\:=? \\ $$ Answered by…
Question Number 15661 by arnabpapu550@gmail.com last updated on 12/Jun/17 $$\int\:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}\mathrm{dx} \\ $$ Commented by arnabpapu550@gmail.com last updated on 13/Jun/17 $$\mathrm{Thanks}\:\mathrm{sir}. \\ $$ Commented by arnabpapu550@gmail.com…
Question Number 146735 by qaz last updated on 15/Jul/21 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…+\frac{\mathrm{1}}{\mathrm{n}}}{\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{2}\right)}=? \\ $$ Answered by Olaf_Thorendsen last updated on 15/Jul/21 $$\mathrm{S}_{\mathrm{N}} \:=\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{N}} {\sum}}\frac{{H}_{{n}}…