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Category: Integration

1-x-dx-

Question Number 87881 by Rio Michael last updated on 06/Apr/20 $$\:\int_{−\infty} ^{\:+\infty} \frac{\mathrm{1}}{{x}}\:{dx}\:=\: \\ $$ Commented by mathmax by abdo last updated on 06/Apr/20 $${the}\:{function}\:{x}\rightarrow\frac{\mathrm{1}}{{x}}\:{is}\:{odd}\:\Rightarrow\int_{−\infty}…

1-sin-x-2cos-x-3-dx-

Question Number 87854 by jagoll last updated on 06/Apr/20 $$\int\:\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{x}+\mathrm{2cos}\:\mathrm{x}+\mathrm{3}}\:\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated on 06/Apr/20 $${I}\:=\int\:\:\frac{{dx}}{\mathrm{2}{cosx}\:+{sinx}\:+\mathrm{3}}\:{we}\:{do}\:{the}\:{changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:\Rightarrow \\ $$$${I}\:=\int\:\:\:\frac{\mathrm{2}{dt}}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)\left(\mathrm{2}\frac{\mathrm{1}−{t}^{\mathrm{2}}…

I-0-pi-4-sin-4x-cos-2-x-tan-4-x-1-dx-

Question Number 87839 by jagoll last updated on 06/Apr/20 $$\mathrm{I}\:=\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{4}}} {\int}}\:\frac{\mathrm{sin}\:\mathrm{4x}}{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\sqrt{\mathrm{tan}\:^{\mathrm{4}} \mathrm{x}+\mathrm{1}}}\:\mathrm{dx} \\ $$ Answered by redmiiuser last updated on 06/Apr/20 $$\sqrt{\mathrm{tan}\:^{\mathrm{4}} {x}+\mathrm{1}}…