Question Number 117945 by bemath last updated on 14/Oct/20 $$\mathrm{f}\left(\mathrm{x}\right)\:=\:\int\:\frac{\mathrm{5x}^{\mathrm{8}} +\mathrm{7x}^{\mathrm{6}} }{\left(\mathrm{2x}^{\mathrm{7}} +\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }\:\mathrm{dx}\:\mathrm{and}\:\: \\ $$$$\mathrm{f}\left(\mathrm{0}\right)\:=\:\mathrm{0}\:,\:\mathrm{then}\:\mathrm{f}\left(\mathrm{1}\right)\:=\:\_\: \\ $$ Commented by bemath last updated on…
Question Number 183450 by cortano1 last updated on 26/Dec/22 $$\:\underset{\mathrm{0}} {\overset{{x}^{\mathrm{2}} } {\int}}\:{f}\left(\mathrm{2}{t}^{\mathrm{3}} −{t}^{\mathrm{2}} −\mathrm{6}\right){dt}\:=\:\mathrm{ln}\:{x}\: \\ $$$$\:{then}\:{f}\left(\mathrm{106}\right)=? \\ $$ Answered by mahdipoor last updated on…
Question Number 117910 by bemath last updated on 14/Oct/20 $$\int\:\mathrm{sin}^{−\mathrm{1}} \left(\sqrt{\mathrm{x}}\right)\:\mathrm{dx}\:=? \\ $$ Commented by bemath last updated on 14/Oct/20 Answered by Lordose last updated…
Question Number 52363 by Necxx last updated on 06/Jan/19 $${integrate}\:\frac{\mathrm{sin}^{\mathrm{2}} {x}\mathrm{cos}^{\mathrm{2}} {x}\:}{{sin}^{\mathrm{3}} {x}+{cos}^{\mathrm{3}} {x}}{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 07/Jan/19 $$=\left(−\mathrm{1}\right)\int\frac{\mathrm{1}−{sin}^{\mathrm{2}} {xcos}^{\mathrm{2}}…
Question Number 52356 by Tawa1 last updated on 06/Jan/19 Commented by tanmay.chaudhury50@gmail.com last updated on 06/Jan/19 Commented by Tawa1 last updated on 07/Jan/19 $$\mathrm{Sir}\:\mathrm{please}\:\mathrm{help}. \\…
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…