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Category: Integration

let-g-x-cosx-1-cos-2x-3-developp-f-at-fourier-serie-

Question Number 98944 by mathmax by abdo last updated on 17/Jun/20 $$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)\:=\frac{\mathrm{cosx}\:+\mathrm{1}}{\mathrm{cos}\left(\mathrm{2x}\right)−\mathrm{3}}\:\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$ Answered by mathmax by abdo last updated on 18/Jun/20 $$\mathrm{g}\left(\mathrm{x}\right)\:=\frac{\mathrm{cosx}+\mathrm{1}}{\mathrm{cos}\left(\mathrm{2x}\right)−\mathrm{3}}\:=\frac{\frac{\mathrm{e}^{\mathrm{ix}} \:+\mathrm{e}^{−\mathrm{ix}}…

calculate-x-1-2x-3-x-2-x-1-dx-

Question Number 98942 by mathmax by abdo last updated on 17/Jun/20 $$\mathrm{calculate}\:\int\:\frac{\mathrm{x}+\mathrm{1}−\sqrt{\mathrm{2x}+\mathrm{3}}}{\mathrm{x}−\mathrm{2}\:+\sqrt{\mathrm{x}+\mathrm{1}}}\:\mathrm{dx} \\ $$ Commented by MJS last updated on 17/Jun/20 $$\mathrm{Sir}\:\mathrm{Abdo},\:\mathrm{do}\:\mathrm{you}\:\mathrm{have}\:\mathrm{an}\:\mathrm{easy}\:\mathrm{solution}? \\ $$$$\mathrm{I}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{it}\:\mathrm{but}\:\mathrm{the}\:\mathrm{constants}\:\mathrm{are}\:\mathrm{getting} \\…

let-x-1-and-1-1-give-the-integral-0-t-x-1-e-t-1-e-t-dt-at-form-of-serie-

Question Number 33353 by caravan msup abdo. last updated on 15/Apr/18 $$\left.{let}\:{x}\in\right]\mathrm{1},+\infty\left[\:{and}\lambda\:\in\left[−\mathrm{1},\mathrm{1}\right]\right. \\ $$$${give}\:{the}\:{integral}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{t}^{{x}−\mathrm{1}} \:{e}^{−{t}} }{\mathrm{1}−\lambda{e}^{−{t}} }\:{dt} \\ $$$${at}\:{form}\:{of}\:{serie}. \\ $$ Commented by…

let-give-S-x-n-0-1-n-x-n-x-gt-0-1-study-the-contnuity-derivsbility-limits-at-0-and-2-we-give-0-e-t-2-dt-pi-2-prove-that-x-gt-0-S-x-1-pi-0-e-

Question Number 33352 by caravan msup abdo. last updated on 15/Apr/18 $${let}\:{give}\:{S}\left({x}\right)=\sum_{{n}\geqslant\mathrm{0}} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{\:\sqrt{{x}+{n}}}\:,{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right){study}\:{the}\:{contnuity}\:,{derivsbility},{limits} \\ $$$${at}\:\mathrm{0}^{+} \:{and}\:+\infty \\ $$$$\left.\mathrm{2}\right)\:{we}\:{give}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{t}^{\mathrm{2}} } {dt}\:=\frac{\sqrt{\pi}}{\mathrm{2}}\:.{prove}\:{that}…