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Category: Integration

Question-149773

Question Number 149773 by Samimsultani last updated on 07/Aug/21 Answered by puissant last updated on 07/Aug/21 $${I}=\int_{\mathrm{0}} ^{\infty} \frac{{cos}\left({ax}\right)}{{x}^{\mathrm{2}} +{b}^{\mathrm{2}} }{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int_{−\infty} ^{+\infty} \frac{{cos}\left({ax}\right)}{{x}^{\mathrm{2}}…

Integrate-the-following-1-a-x-x-dx-2-dx-sin-x-3-2-cos-x-

Question Number 84234 by niroj last updated on 10/Mar/20 $$\:\:\boldsymbol{\mathrm{Integrate}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}: \\ $$$$\:\:\:\mathrm{1}.\:\int\sqrt{\frac{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}}}\:\boldsymbol{\mathrm{dx}} \\ $$$$\:\:\:\mathrm{2}.\int\:\:\frac{\boldsymbol{\mathrm{dx}}}{\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}\left(\mathrm{3}+\mathrm{2}\:\boldsymbol{\mathrm{cos}}\:\boldsymbol{\mathrm{x}}\right)} \\ $$$$\: \\ $$ Commented by mathmax by abdo last updated…

Question-149739

Question Number 149739 by iloveisrael last updated on 07/Aug/21 Answered by Olaf_Thorendsen last updated on 07/Aug/21 $$\lambda\:=\:\int_{\mathrm{0}} ^{\pi} {x}\mathrm{sin}^{\mathrm{9}} {x}\:{dx}\:\:\:\left(\mathrm{1}\right) \\ $$$$\lambda\:=\:\int_{\pi} ^{\mathrm{0}} \left(\pi−{u}\right)\mathrm{sin}^{\mathrm{9}} \left(\pi−{u}\right)\:\left(−{du}\right)…

dx-x-x-4-1-

Question Number 18650 by thukada last updated on 26/Jul/17 $$\int{dx}/{x}\sqrt{{x}^{\mathrm{4}} −\mathrm{1}} \\ $$ Answered by sma3l2996 last updated on 26/Jul/17 $${A}=\int\frac{{dx}}{{x}\sqrt{{x}^{\mathrm{4}} −\mathrm{1}}} \\ $$$${let}\:\:{t}=\sqrt{{x}^{\mathrm{4}} −\mathrm{1}}\Rightarrow{dt}=\frac{\mathrm{2}{x}^{\mathrm{3}}…

dx-x-3-4-x-3-1-3-

Question Number 84170 by jagoll last updated on 10/Mar/20 $$\int\:\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{3}} \:\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{4}−\mathrm{x}^{\mathrm{3}} }}\:?\: \\ $$ Answered by john santu last updated on 10/Mar/20 $$\int\:\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{4}} \:\sqrt[{\mathrm{3}\:\:}]{\frac{\mathrm{4}}{\mathrm{x}^{\mathrm{3}} }−\mathrm{1}}}\:=\:…