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Category: Integration

let-give-I-m-a-0-cos-mx-1-x-2-x-2-a-2-dx-1-verify-that-I-m-1-lim-a-1-I-m-a-2-find-the-value-of-0-x-sin-mx-1-x-2-2-dx-

Question Number 28985 by abdo imad last updated on 02/Feb/18 $${let}\:{give}\:{I}_{{m},{a}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{cos}\left({mx}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)}{dx} \\ $$$$\left.\mathrm{1}\right){verify}\:{that}\:{I}_{{m},\mathrm{1}} ={lim}_{{a}\rightarrow\mathrm{1}} \:{I}_{{m},{a}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}\:{sin}\left({mx}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}}…

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) \\…