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Category: Integration

tan-x-sin-x-cos-x-dx-

Question Number 94510 by i jagooll last updated on 19/May/20 $$\int\:\frac{\sqrt{\mathrm{tan}\:{x}}}{\mathrm{sin}\:{x}.\mathrm{cos}\:{x}}{dx}\: \\ $$ Commented by PRITHWISH SEN 2 last updated on 19/May/20 $$\int\frac{\mathrm{sec}^{\mathrm{2}} \mathrm{x}.\sqrt{\mathrm{tanx}}}{\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\:\:\mathrm{now}\:\mathrm{put}\:\mathrm{tanx}=\mathrm{t}^{\mathrm{2}} \\…

1-4sin-x-3cos-x-dx-evaluate-

Question Number 160013 by Odhiambojr last updated on 23/Nov/21 $$\int\frac{\mathrm{1}}{\mathrm{4}{sin}\:{x}+\mathrm{3}{cos}\:{x}}{dx} \\ $$$${evaluate} \\ $$ Commented by tounghoungko last updated on 23/Nov/21 $$\:\:{I}=\int\:\frac{{dx}}{\mathrm{4sin}\:{x}+\mathrm{3cos}\:{x}}\:=? \\ $$$$\mathrm{4sin}\:{x}+\mathrm{3cos}\:{x}=\mathrm{5}\left(\frac{\mathrm{4}}{\mathrm{5}}\mathrm{sin}\:{x}+\frac{\mathrm{3}}{\mathrm{5}}\mathrm{cos}\:{x}\right) \\…

1-prove-that-x-0-x-x-2-2-ln-1-x-x-2-find-lim-n-k-1-n-1-1-k-2-n-2-n-

Question Number 28890 by abdo imad last updated on 31/Jan/18 $$\left.\mathrm{1}\right)\:{prove}\:{that}\:\forall\:{x}\geqslant\mathrm{0}\:\:\:{x}\:−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\leqslant{ln}\left(\mathrm{1}+{x}\right)\leqslant{x} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\prod_{{k}=\mathrm{1}} ^{{n}} \left(\mathrm{1}\:+\:\frac{\mathrm{1}}{{k}^{\mathrm{2}} +{n}^{\mathrm{2}} }\right)^{{n}} . \\ $$ Terms of Service…

find-arcsin-x-x-2-dx-

Question Number 28887 by abdo imad last updated on 31/Jan/18 $${find}\:\int\:\:{arcsin}\left(\sqrt{\frac{{x}}{{x}+\mathrm{2}}}\right){dx}. \\ $$ Commented by abdo imad last updated on 02/Feb/18 $${let}\:{use}\:{the}\:{ch}.{arcsin}\left(\sqrt{\:\frac{{x}}{{x}+\mathrm{1}}}\:\right)={t}\:\Leftrightarrow\sqrt{\frac{{x}}{{x}+\mathrm{1}}}\:={sint} \\ $$$$\Leftrightarrow\frac{{x}}{{x}+\mathrm{1}}={sin}^{\mathrm{2}} {t}\:\Leftrightarrow{x}={xsin}^{\mathrm{2}}…