Question Number 144000 by bluberry508 last updated on 20/Jun/21 $$\mathrm{prove}\:\mathrm{that}\: \\ $$$$ \\ $$$$\forall_{{m}} \in\mathbb{N}\:,\:{a}_{{k}} ,{b}_{{k}} \in\mathbb{R} \\ $$$$\mathrm{cos}\:^{\mathrm{2}{m}} {x}\:=\underset{{k}=\mathrm{1}} {\overset{{m}} {\sum}}{a}_{{k}} \mathrm{cos}\:\mathrm{2}{kx} \\ $$$$\mathrm{cos}\:^{\mathrm{2}{m}−\mathrm{1}}…
Question Number 12908 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 06/May/17 Answered by 433 last updated on 07/May/17 $$\int_{\sqrt{\mathrm{2}}} ^{\mathrm{2}} \left(\frac{{x}^{\mathrm{2}} }{{x}+\left[{x}+\mathrm{1}\right]}\right){dx}+\int_{\mathrm{2}} ^{\sqrt{\mathrm{5}}} \left(\frac{{x}^{\mathrm{2}} }{{x}+\left[{x}+\mathrm{1}\right]}\right){dx}= \\ $$$$\int_{\sqrt{\mathrm{2}}}…
Question Number 143952 by akolade last updated on 19/Jun/21 Answered by Olaf_Thorendsen last updated on 20/Jun/21 $$\mathrm{C}\:=\:\int\frac{\mathrm{cosh}{x}}{\mathrm{cosh}{x}+\mathrm{sinh}{x}}\:{dx} \\ $$$$\mathrm{S}\:=\:\int\frac{\mathrm{sinh}{x}}{\mathrm{cosh}{x}+\mathrm{sinh}{x}}\:{dx} \\ $$$$\mathrm{C}+\mathrm{S}\:=\:\int{dx}\:=\:{x}+\mathrm{cst}\:\:\:\:\:\left(\mathrm{1}\right) \\ $$$$\mathrm{C}−\mathrm{S}\:=\:\int\frac{\mathrm{cosh}{x}−\mathrm{sinh}{x}}{\mathrm{cosh}{x}+\mathrm{sinh}{x}}\:{dx} \\ $$$$\mathrm{C}−\mathrm{S}\:=\:\int\frac{\left(\mathrm{cosh}{x}−\mathrm{sinh}{x}\right)^{\mathrm{2}}…
Question Number 143932 by Ar Brandon last updated on 19/Jun/21 Answered by mathmax by abdo last updated on 19/Jun/21 $$\left.\mathrm{1}\right)\:\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\mathrm{t}^{\mathrm{2}} } \mathrm{dt}\:\:\:\:\:\:\Rightarrow\mathrm{I}=\int_{\mathrm{0}} ^{\mathrm{a}}…
Question Number 12826 by malwaan last updated on 03/May/17 $$\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{1}:\:\:\mathrm{0}<\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\mathrm{x}\sqrt{\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}<\:\frac{\pi^{\mathrm{2}} }{\mathrm{32}} \\ $$$$\mathrm{2}:\:\frac{\mathrm{1}}{\mathrm{2}}<\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}\:\mathrm{dx}\:<\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\ $$$$\mathrm{3}:\:\mathrm{0}<\int_{\mathrm{100}\pi} ^{\mathrm{200}\pi} \:\frac{\mathrm{cos}\:\mathrm{x}}{\mathrm{x}}\:\mathrm{dx}\:<\frac{\mathrm{1}}{\mathrm{100}\pi} \\ $$…
Question Number 143892 by mathmax by abdo last updated on 19/Jun/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{cos}^{\mathrm{4}} \left(\mathrm{2x}\right)}{\left(\mathrm{x}^{\mathrm{4}} \:−\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$ Terms of Service Privacy Policy…
Question Number 143889 by mnjuly1970 last updated on 19/Jun/21 $$ \\ $$$$\:\:\:\:\:\:{A}\:\:{Challanging}\:\:{Integral}: \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\Phi\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{{log}\left({x}\right).{log}\left(\mathrm{1}+{x}\right)}{\mathrm{1}−{x}}{dx} \\ $$$$ \\ $$$$ \\ $$ Answered…
Question Number 12804 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 01/May/17 Commented by tawa last updated on 01/May/17 Commented by tawa last updated on 01/May/17 Commented by…
Question Number 78334 by john santu last updated on 16/Jan/20 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\left[\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{cos}\:{x}\right)+\mathrm{sin}^{\mathrm{2}} \:\left(\mathrm{sin}\:{x}\right)\:\right]\:{dx} \\ $$ Commented by MJS last updated on 16/Jan/20 $$\mathrm{we}\:\mathrm{cannot}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{integral}\:\mathrm{but}\:\mathrm{we}\:\mathrm{can}…
Question Number 143850 by cesarL last updated on 18/Jun/21 Terms of Service Privacy Policy Contact: info@tinkutara.com