Question Number 154641 by cesarL last updated on 20/Sep/21 $$\int\frac{\mathrm{1}−\sqrt{{x}}}{\:\sqrt{\mathrm{1}−{x}}}{dx} \\ $$ Answered by puissant last updated on 20/Sep/21 $${u}=\sqrt{\mathrm{1}−{x}}\rightarrow\:{u}^{\mathrm{2}} =\mathrm{1}−{x}\:\rightarrow\:{x}=\mathrm{1}−{u}^{\mathrm{2}} \\ $$$$\Rightarrow\:{dx}=−\mathrm{2}{udu}\: \\ $$$${I}=\int\frac{\mathrm{1}−\sqrt{\mathrm{1}−{u}^{\mathrm{2}}…
Question Number 154621 by liberty last updated on 20/Sep/21 $$\:\int\:\frac{\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}{{x}^{\mathrm{2}} +{x}}\:{dx}\: \\ $$ Commented by mathdanisur last updated on 20/Sep/21 $$=\int\:\underset{} {\underbrace{\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}}}}\:+\int\underset{} {\underbrace{\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}}…
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Question Number 89052 by M±th+et£s last updated on 15/Apr/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{x}}{{tan}\left({x}\right)}{dx} \\ $$ Commented by abdomathmax last updated on 15/Apr/20 $${I}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{x}}{{tanx}}{dx}\:\Rightarrow{I}\:=_{{tanx}={t}} \:\:\:\int_{\mathrm{0}}…
Question Number 89025 by M±th+et£s last updated on 14/Apr/20 $$\int\frac{\mathrm{3}^{{x}} +\mathrm{4}^{{x}} }{\mathrm{5}^{{x}} }{dx} \\ $$ Answered by $@ty@m123 last updated on 14/Apr/20 $$\int\left(\frac{\mathrm{3}}{\mathrm{5}}\right)^{{x}} {dx}+\int\left(\frac{\mathrm{4}}{\mathrm{5}}\right)^{{x}} {dx}…
Question Number 23485 by guramritsingh22@gmail.com last updated on 31/Oct/17 $$\frac{\mathrm{1}}{\mathrm{cos}\:\left({x}−{a}\right)\mathrm{cos}\:\left({x}−{b}\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 154557 by talminator2856791 last updated on 19/Sep/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{1}}{\left(\underset{{n}=\mathrm{0}} {\overset{\lceil{x}^{\mathrm{2}} \rceil} {\sum}}\:{n}\right)^{\mathrm{2}} }\:{dx} \\ $$$$\: \\ $$ Terms of Service…
Question Number 88973 by M±th+et£s last updated on 14/Apr/20 $$\int\frac{\mathrm{3}{tan}\left({x}\right)}{\mathrm{2}{sin}^{\mathrm{2}} \left({x}\right)+\mathrm{5}{cos}^{\mathrm{2}} \left({x}\right)+{sec}\left({x}\right)}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 23432 by gopikrishnan005@gmail.com last updated on 30/Oct/17 $$\int_{\mathrm{0}} ^{{a}} {f}\left({x}\right){dx}= \\ $$ Answered by Joel577 last updated on 31/Oct/17 $$\mathrm{Let}\:{F}\left({x}\right)\:\mathrm{is}\:\mathrm{an}\:\mathrm{anti}\:\mathrm{derivative}\:\mathrm{of}\:{f}\left({x}\right) \\ $$$${I}\:=\:\underset{\mathrm{0}} {\overset{{a}}…
Question Number 23433 by gopikrishnan005@gmail.com last updated on 30/Oct/17 $$\int_{\mathrm{0}} ^{\infty} {X}^{\mathrm{6}} {e}^{−{x}/\mathrm{2}} {dx}= \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com