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Category: Integration

ln-sinx-dx-

Question Number 154673 by Study last updated on 20/Sep/21 $$\int{ln}\left({sinx}\right){dx}=? \\ $$ Commented by puissant last updated on 20/Sep/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({sinx}\right){dx}=−\frac{\pi}{\mathrm{2}}{ln}\mathrm{2}.. \\ $$ Commented…

cos-2x-sec-x-cos-2-x-dx-

Question Number 89123 by john santu last updated on 15/Apr/20 $$\int\:\frac{\mathrm{cos}\:\mathrm{2}{x}}{\mathrm{sec}\:{x}−\mathrm{cos}\:^{\mathrm{2}} {x}}\:{dx}\:? \\ $$ Commented by MJS last updated on 15/Apr/20 $$\mathrm{Weierstrass}\:\mathrm{leads}\:\mathrm{to} \\ $$$$−\int\frac{{t}^{\mathrm{6}} −\mathrm{7}{t}^{\mathrm{4}}…

1-x-1-x-dx-

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}}…

x-2-x-1-x-2-x-dx-

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}}…

0-pi-2-x-tan-x-dx-

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}}…

3-x-4-x-5-x-dx-

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}…

0-1-n-0-x-2-n-2-dx-

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…