Question Number 183382 by mathlove last updated on 25/Dec/22 Commented by CElcedricjunior last updated on 25/Dec/22 $$\int\frac{\boldsymbol{{x}}+\mathrm{1}}{\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{6}\boldsymbol{{x}}+\mathrm{9}}\boldsymbol{{dx}}=\frac{\mathrm{1}}{\mathrm{4}}\int\frac{\mathrm{4}\boldsymbol{{x}}+\mathrm{6}}{\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{6}\boldsymbol{{x}}+\mathrm{9}}\boldsymbol{{dx}}−\frac{\mathrm{1}}{\mathrm{4}}\int\frac{−\mathrm{2}}{\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{6}\boldsymbol{{x}}+\mathrm{9}}\boldsymbol{{dx}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{4}}\boldsymbol{{ln}}\mid\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{6}\boldsymbol{{x}}+\mathrm{9}\mid−\frac{\mathrm{1}}{\mathrm{4}}\int\frac{{dx}}{\left(\boldsymbol{{x}}+\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}} +\frac{\mathrm{9}}{\mathrm{4}}}\:\boldsymbol{{t}}=\frac{\mathrm{2}\boldsymbol{{x}}+\mathrm{3}}{\mathrm{3}} \\…
Question Number 117841 by john santu last updated on 14/Oct/20 $$\int\:\mathrm{ln}\:\left(\mathrm{1}−{e}^{−\mathrm{2}{x}} \right)\:{dx}\:=? \\ $$ Answered by MJS_new last updated on 14/Oct/20 $$\int\mathrm{ln}\:\left(\mathrm{1}−\mathrm{e}^{−\mathrm{2}{x}} \right)\:{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{e}^{−\mathrm{2}{x}}…
Question Number 117817 by peter frank last updated on 13/Oct/20 Commented by Lordose last updated on 13/Oct/20 $$\mathrm{A}\:=\:\int\mathrm{a}^{\sqrt{\mathrm{x}}} \mathrm{dx} \\ $$$$\mathrm{u}=\sqrt{\mathrm{x}}\:\Rightarrow\:\mathrm{dx}=\mathrm{2udu} \\ $$$$\mathrm{A}\:=\int\mathrm{2ua}^{\mathrm{u}} \mathrm{du} \\…
Question Number 117811 by Lordose last updated on 13/Oct/20 $$\int_{\:\mathrm{0}} ^{\:\boldsymbol{\pi}} \boldsymbol{\mathrm{ln}}\mid\boldsymbol{\mathrm{sinh}}\left(\boldsymbol{\mathrm{x}}\right)\mid\boldsymbol{\mathrm{dx}} \\ $$ Answered by mindispower last updated on 13/Oct/20 $$=\int_{\mathrm{0}} ^{\pi} {ln}\left({sh}\left({x}\right)\right){dx} \\…
Question Number 117806 by mnjuly1970 last updated on 13/Oct/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:{calculus}… \\ $$$$\:\:\:\:{i}\:::\:\:\:\mathrm{1}\:+\frac{\mathrm{4}}{\mathrm{9}}+\frac{\mathrm{9}}{\mathrm{36}}+\frac{\mathrm{16}}{\mathrm{100}}+…=\:?? \\ $$$$\:\:\:\:\:{ii}::\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {x}^{\mathrm{2}} {cot}\left({x}\right)\:{dx}=?? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$$$ \\ $$ Commented by…
Question Number 183320 by mathlove last updated on 25/Dec/22 $$\underset{\mathrm{0}} {\int}^{\frac{\pi}{\mathrm{2}}} \frac{{dx}}{{cox}\frac{{x}}{\mathrm{2}}\centerdot{cos}\frac{{x}}{\mathrm{2}^{\mathrm{2}} }\centerdot\centerdot\centerdot\centerdot\centerdot{cos}\frac{{x}}{\mathrm{2}^{{n}} }}=? \\ $$ Answered by Vynho last updated on 28/Dec/22 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 52233 by de best last updated on 04/Jan/19 $${please}\:{can}\:{you}\:{help}\:{me}\:{with}\:{this}\: \\ $$$${caculus}:\:\int\frac{\mathrm{1}}{{cos}^{\mathrm{2}} {x}}\:{dx} \\ $$ Answered by MJS last updated on 04/Jan/19 $$\mathrm{this}\:\mathrm{is}\:\mathrm{a}\:\mathrm{standard}\:\mathrm{integral} \\…
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Question Number 183279 by cortano1 last updated on 24/Dec/22 $$\:\:\int\:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\left(\mathrm{tan}\:{x}−\mathrm{cot}\:{x}\right)^{\mathrm{3}} }\:{dx}\:=? \\ $$ Answered by MJS_new last updated on 24/Dec/22 $$\mathrm{with}\:{t}=\mathrm{tan}\:\frac{{x}}{\mathrm{2}}\:\mathrm{we}\:\mathrm{get} \\ $$$$−\mathrm{16}\int\frac{{t}^{\mathrm{3}} \left({t}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{3}}…
Question Number 52197 by maxmathsup by imad last updated on 04/Jan/19 $${calculate}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\frac{{cosx}\:−{sinx}}{\mathrm{2}\:+{sin}\left(\mathrm{2}{x}\right)}{dx} \\ $$$$ \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 04/Jan/19…